Risk Analytics, Real Options and Optimal Decisions

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Zili Zhu, Thomas Sneddon, Colin O’Hare, Xiaolin Luo, Pavel Shevchenko, Zili Zhu, Thomas Sneddon, Colin O’Hare, Xiaolin Luo, Pavel Shevchenko, Chenming Bao, Alec Stephenson, Peter Toscas

Chenming Bao, Alec Stephenson, Peter Toscas

Quantitative Modelling for

Decumulation

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Decumulation

Decumulation Phase: Four Projects

Phase: Four Projects

1.

1. ATO Data Analysis on SMSF and APRA Fund Holder BehaviourATO Data Analysis on SMSF and APRA Fund Holder Behaviour 2.

2. Simulation of Uncertainty for Pension Analysis (SUPA): forecasting Simulation of Uncertainty for Pension Analysis (SUPA): forecasting ruin years

ruin years 3.

3. Pricing Algorithm for New Guaranteed Investment Products: Pricing Algorithm for New Guaranteed Investment Products: GMWB and GMDB

GMWB and GMDB 4.

4. Optimal Decisions for Better Retirement: Dynamic Portfolio Optimal Decisions for Better Retirement: Dynamic Portfolio Analytics for Superannuation Life

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1. ATO data analysis

ATO data analysis

o 150,000 taxpayers

o Data points: age, gender, SMSF account balance, SMSF contributions,

SMSF earnings SMSF withdrawals APRA account balance APRA SMSF earnings, SMSF withdrawals, APRA account balance, APRA contributions

o Capacity to investigate withdrawal rates, personal (non‐mandatory)

contribution rates account balance annual returns by category (gender contribution rates, account balance annual returns by category (gender, age, income quantile, fund type) o 10 year data from 2004 to 2014 o 55‐99 years of age o 27% SMSF only, 39% APRA only, and 34% both SMSF&APRA • 440K, 48K, SMSF Data 50 000

APRA Data Balances

10^ 6 0 00 30000 F requency 00 3 0000 F re q uenc y D o ll ar s 10^ 4 1 0^ 5 01 0 0 Age 55 58 61 64 67 70 73 76 79 82 85 88 91 94 01 0 0 Age 55 58 61 64 67 70 73 76 79 82 85 88 91 94 SMSF APRA 10^ 3

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1. The median average values of super funds

Super fund performances when member contributions are

also counted:

0 .2 5 SMSF SMSF

Performance rate per year: Balance changes with age:

0. 15 0 g  bt bt 1  SMSF APRA 0 .1 5 0 .2 5 Logdi ff SMSF APRA 0. 0 5 A ver a g e lo 0. 05 0 A v er age 55 60 65 70 75 80 85 -0 .0 5 Age 2006 2008 2010 2012 2014 -0 .0 5 Calendar Year

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1. Fund performances excluding member contribution

The median average:

Performance rate per year: Balance moves with age:

0 0 1 .0 5 1 .1 0 ct  bt 1 SMSF_APRA 41 .0 8 ct  bt 1 SMSF APRA 0. 90 0. 9 5 1. 0 A ve ra g e  bt  1. 00 1. 0 A ve ra ge  bt  2006 2008 2010 2012 2014 0. 85 Calendar Year 55 60 65 70 75 80 85 0. 96 Age Risk Analytics, Real‐Options and Optimal Decisions CSIRO

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1. Account balances change during 2006 and 2013

SMSF Balances 2006 0 0 APRA Balances 2006 1 00 0000 D o lla rs 0 000 0 10000 0 D o lla rs 0 0 1 0 0000 1 58 60 62 64 66 68 70 72 74 76 78 1000 0 1 0 58 60 62 64 66 68 70 72 74 76 100 0 100 0 58 60 62 64 66 68 70 72 74 76 SMSF Balances 2013 APRA Balances 2013 0 00 o lla rs 1000 000 la rs 0000 0 1000 0 D o 0 1000 00 Do l 1 0000 1 0

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1. SMSF & APRA Performances 2006‐2013

2006 2009 2012 .01 .1 1 .2 2006 bt  ct  bt 1 SMSF APRA 01 .1 1 .2 2009 bt  ct  bt 1 SMSF APRA 0 1. 1 1 .2 2012 bt  ct  bt 1 SMSF APRA 55 60 65 70 75 80 85 0. 8 0 .9 1 . A ve ra ge  b 55 60 65 70 75 80 85 0. 8 0 .9 1. A ve ra ge  b 55 60 65 70 75 80 85 0. 8 0 .9 1 .0 A v er age  b Age 11 .2 2007 1 SMSF APRA 55 60 65 70 75 80 85 Age .11 .2 2010 1 SMSF APRA 55 60 65 70 75 80 85 Age .1 1 .2 2013 t 1 SMSF APRA 0. 9 1 .0 1. A ve ra ge  bt  ct  bt 0. 9 1 .0 1 . A ver age  bt  ct  bt 0. 9 1 .0 1 A ver age  bt  ct  bt 55 60 65 70 75 80 85 0. 8 Age 1 1. 2 2008 1 SMSF APRA 55 60 65 70 75 80 85 0. 8 Age 1 1. 2 2011 1 SMSF APRA 55 60 65 70 75 80 85 0. 8 Age 0. 8 0 .9 1. 0 1 .1 A v er age  bt  ct  bt1 0. 8 0 .9 1. 0 1 .1 A v e rag e  bt  ct  bt1 55 60 65 70 75 80 85 Age 55 60 65 70 75 80 85 Age Risk Analytics, Real‐Options and Optimal Decisions CSIRO

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1. SMSF Withdraw Rates For Age Groups

SMSF Withdrawals Ages 70 74 SMSF Withdrawals Ages 60-64 50 000 SMSF Withdrawals Ages 70-74 15000 F re que nc y 0 0 300 00 F requency 5000 10000 Withdrawal Proportion 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0 100 Withdrawal Proportion 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0 SMSF Withdrawals Ages 75+ SMSF Withdrawals Ages 65-69 000 SMSF Withdrawals Ages 75+ 800 0 Fr e que ncy 1 500 0 2 5 Fr e que ncy 00 4 0 0 0 60 00 Withdrawal Proportion 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0 500 0 Withdrawal Proportion 0.00 0.05 0.10 0.15 0.20 0.25 0.30 02 0

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1. SMSF withdrawals according to account balances

0% 20% 40% 60% 80% 100% 0 203000 430000 720000 1280000 5000000 0. 04 0. 0 6 raw a l P rop or ti o n 0. 06 0. 08 0. 10 Medium Balance a w a l P ro por ti on 60 65 70 75 80 85 90 0. 00 0 .02 Av er age W it h d r 60 65 70 75 80 85 0. 00 0. 02 0. 0 4 A v er ag e W it h dr a 60 65 70 75 80 85 90 Age 0. 08 0. 1 0

Very Low Balance

o po rt io n Age 0. 08 0. 10 High Balance o po rt io n 0. 02 0. 04 0. 06 A v er ag e W it hdr aw al P ro 0 .02 0 .04 0. 06 A v e ra ge W it h d raw al P ro 60 65 70 75 80 85 0. 0 0 Age 0. 10 Low Balance n 60 65 70 75 80 85 0. 00 Age A 0. 10

Very High Balance

n 2 0. 04 0. 06 0. 08 g e W it hdr aw al P ropor ti o n 2 0. 04 0. 06 0. 08 g e W it h dr a w al P rop or ti o n 60 65 70 75 80 85 0. 00 0. 0 2 Age Av e ra g 60 65 70 75 80 85 0. 00 0. 0 2 Age Av e ra g

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1. The Closure Rates of SMSF & APRA Funds

0

80

.1

0

SMSF Closure Data (SMSF Only)

0

80

.1

0

APRA Closure Data (APRA Only)

0. 04 0. 06 0 .0 P ropor ti on 0 .0 4 0. 06 0. 0 Pr op or ti o n 55 60 65 70 75 80 85 0. 00 0. 02 55 60 65 70 75 80 85 0. 00 0. 02 Age Age 0. 08 0 .10

SMSF Closure Data (Both Only)

0.08

0

.10

APRA Closure Data (Both Only)

2 0. 04 0. 06 P ropor ti on 2 0 .04 0.0 6 P rop or tio n 55 60 65 70 75 80 85 0 .00 0. 0 2 Age 55 60 65 70 75 80 85 0.00 0 .0 2 Age

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1. The Next Step

• Negotiation with DHS/DSS for more comprehensive data

o Assets and bank accounts of full/part pension members

o Medical expenses via Medicare

• More detailed data from ATO and address concerns on dataMore detailed data from ATO and address concerns on data

confidentiality.

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2. 2. Decumulation

Decumulation Phase: Using SUPA model for

Phase: Using SUPA model for

simulation

The SUPA model projects long-term

economic behaviour: applies

established stochastic asset model

(Wilki d l)

(Wilkie model)

Output from SUPA is used for

M t C l i l ti b f

Monte Carlo simulation: any number of

paths of desired time span

Additional models extend SUPA: Additional models extend SUPA: models for withdrawals, death

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2. SUPA can answer questions in

decumulation

decumulation phase

phase

decumulation

decumulation phase

phase

 M b ’ ti  Member’s questions: • Probability of ruin of individual’s super (before x years or before death) • $ needed in super fund at retirement (to last for x years or until death)$ p ( y ) • % of salary that should be contributed to fund to achieve some objective • Optimal investment strategies to reach $ amount or avoid ruin • Annuity‐related purchase/investment strategies  Fund level questions:

• Probability of ruin of an entire group fund • Probability of ruin of an entire group fund • $ needed in fund at given time (liquidity risk)

• % aggregate fund balance that fund should collect • Optimal investment strategy (from fund mgmt POV)

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2. Progress on SUPA since last meeting

1. Addition of capacity to have different asset allocations for pre‐ retirement as opposed to post retirement

retirement as opposed to post‐retirement

2. Addition of variable retirement age = can alter retirement age and immediately see the effect this has on retirement outcomes and immediately see the effect this has on retirement outcomes 3. Year‐upon‐year variability of mandatory contribution rate = can

alter the rate to immediately see the effect of this can have a alter the rate to immediately see the effect of this, can have a different rate for each year into the future rather than a set rate 4. Addition of taxation arrangements – investment earnings tax and 4. Addition of taxation arrangements investment earnings tax and

contributions tax

5. Addition of age pension income = can determine when super g p p fund balance exhausted in presence of pension income

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2. Front

2. Front‐‐page of

page of SUPA

SUPA Model Output

Model Output

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2. Example: Impact of altered mandatory

contribution rate schedule (September 2014)

Assumptions: Starting annual expense $42,254.00 Assumptions: •To right

•Mandatory contribution rate

Asset Allocation (constant)

Australian Equities 35.00% International Equities 25 00%

•Mandatory contribution rate

schedule for comparison is pre-September schedule vs new schedule (see below)

International Equities 25.00% Domestic Bonds 12.00% International Bonds 8.00%

Cash 20.00%

schedule (see below) _{Starting Age} ₂₅

Starting Salary $54,425 YEAR 2014-2015 2015-2016 2016-2017 2017-2018 2018-2019 2019-2020 2020-2021 2021-2022 2022-2023 2023-2024 2024-2025 2025-2026+ Pre-2014 9.5% 10% 10.5% 11% 11.5% 12% 12% 12% 12% 12% 12% 12% Pre 2014 9.5% 10% 10.5% 11% 11.5% 12% 12% 12% 12% 12% 12% 12% New 9.5% 9.5% 9.5% 9.5% 9.5% 9.5% 9.5% 10% 10.5% 11% 11.5% 12%

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2.

2. Example: Impact of altered mandatory

Example: Impact of altered mandatory

t ib ti

t

h d l (S

t

b

2014)

t ib ti

t

h d l (S

t

b

2014)

contribution rate schedule (September 2014)

Comments: Statistic Old CR structure New CR structure Difference

Comments:

• Can readily alter CR schedule to

immediately see

Average fund length

post-retirement (years) 28.2186 26.9537 -1.2649 Standard deviation of

fund length

post-impact

• Can also alter retirement age to immediately see

fund length post

retirement 12.0198 11.9060 -0.1138 Probability of super

funds ruin before death 23.49% 26.00% +2.51% E t d b f

immediately see impact

• Results align with recent literature

Expected number of years between ruin and

death 1.8083 2.04 +0.23 Fund balance at retirement at 65 (current surrounding impact of CR changes ( $) $781,941.92 $749,734.84 -$32,207.10 Fund balance at retirement at 65 (nominal $) $2,160,401.40 $2,071,202.09 -$89,199.30 Fund balance at

mid-2025 (current $) $87,713.68 $77,205.64 -$10,508.00 Fund balance at

mid-2025 (nominal $) $115,970.94 $102,078.70 -$13,892.20

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2. Next steps for SUPA

Additional features:

• Salary inflation based upon cohort

Deliverables:

• 2 papers in final draft process:

salary inflation experience (rather than wage index)

• Withdrawals based upon % of super

f d b l ( i bl i h ) d

p p p

o SUPA model as a new

approach for retirement income assessment

fund balance (variable with age) and income replacement rate (in

addition to ASFA retirement

t d d l l)

o Applications of the SUPA

model in retirement income assessment

C i f d l il bl

standard level)

• Capacity to alter asset allocation on

an annual basis

• Current version of model available

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3. Products with Protected Capital, Income and Death Benefit

•Variable annuities with guarantees (GMWB GLWB )

•Variable annuities with guarantees (GMWB, GLWB,…) also marketed as various wealth protection/guarantee retirement products •Guarantee to return the entire initial investment through cash withdrawals during contract or guarantee of income (even for market downturns when ( investment account depleted) •Returns remaining portfolio at maturity (gain from k t id ) market upside) •Withdrawals can be fixed or flexible subject to penalty if contract rate is exceeded or contract is terminated l f i bl i i i earlier •Fixed term or lifetime contract duration D h b fi b dd d f f b h Sales of Variable Annuities in USA, Source: Milliman Q3 2014 •Death benefit can be added for extra fee but cheaper than separate life insurance Risk Analytics, Real‐Options and Optimal Decisions CSIRO

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3. Market for advanced products and challenges

•USA, Japan and UK: significant market for variable annuities (e.g. $150b in US 2013) I J l 2014 F th ht l h d F R ti t F d ti VA GLWB ith •In July 2014, Forethought launched ForeRetirement Foundation VA: GLWB with fees increase/decrease based on 10‐year Treasure rate. •Australia market – early stage: e.g. MLC protected wealth and protected income products; AMP North Protected Retirement guarantee.

•Pricing sophisticated products with equity risk, interest rate risk, systematic

mortality risk and human behaviour is a difficult numerical/mathematical problem especially in the case of flexible/dynamic withdrawals.

•Existing products are limited by numerical difficulties; e.g. industry practice is to use Monte Carlo forward simulation while correct pricing for flexible withdrawals use Monte Carlo forward simulation while correct pricing for flexible withdrawals requires backward solution for optimal control problem. Quoted academic

literature computing time is 20‐40 hours per price in the case of flexible

ithd l Al i li ti t h ti d l ( l l lk) d

withdrawals. Also, over‐simplistic stochastic models (e.g. lognormal walk) are used.

•Some industry approaches restrict product features, underestimate risks or

overpricingp g. E.g. assumption of pre‐determined withdrawals, Normal distribution g p p , for risky asset returns, deterministic interest rate, constant volatility, mortality from simple life table (ignoring systemic mortality risk)

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3. CSIRO pricing engine for advanced retirement products

•Pricing combined death and minimum withdrawal guarantees with flexible withdrawals

•CSIRO engine capability: pricing accurately and in real time; can be used to develop new wealth retirement products, portfolio risk management and

develop new wealth retirement products, portfolio risk management and

hedging/trading strategies for competitive advantage

•Pricing different guarantee features – mathematics is similar to pricing exotic

ti CSIRO ti i i i R dit f FX ti h li ti

options: CSIRO exotic pricing engine Reditus for FX exotics – showcase application

500 600 static/fixed withdrawal optimal withdrawal (10% penalty) ₄₀ 45 t (bp) GMWDB, male 300 400 ir fe e (bp) optimal withdrawal (5% penalty) 20 25 30 35 be n e fi t pa ym e n t separate life insurance, male 100 200 Fa 5 10 15 20 Q ua rt e rl y de at h 0 5% 7% 9% 11% 13% 15% minimum guaranteed withdrawal rate (%)

Australia data: life table and interest rate curve, male 60 years old, 20% volatility 0 5% 7% 9% 11% 13% 15% minimum guaranteed withdrawal rate (%) Q Australia data: life table and interest rate curve, male 60 years old, 20% volatility Risk Analytics, Real‐Options and Optimal Decisions CSIRO

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3. CSIRO prototype software: GMWB and GMDB

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3. Extensions of current pricing algorithm

• Adding features of existing products on the market and comparing with market prices

comparing with market prices

• Mortality risk factor models to account for mortality

systematic (undiversified) risk: model estimation and use for systematic (undiversified) risk: model estimation and use for annuity pricing • Pricing annuity type products with many underlying stochastic variables (interest rate, volatility, mortality) • Hedging annuity products and portfolio management Risk Analytics, Real‐Options and Optimal Decisions CSIRO

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4. 4. Dynamic Portfolio Analytics for Superannuation

Dynamic Portfolio Analytics for Superannuation

Life

Life Cycle

Cycle

Life

Life‐‐Cycle

Cycle

Objectives: Objectives:

• Link the empirical research findings to strategic financial t e e p ca esea c d gs to st ateg c a c a planning;

• Generic/flexible multi-period dynamic portfolio optimization engine:

o Simulation based & data driven; o Asset/liability model free;

o Asset/liability model free;

o Provide recommendation of fund management decisions.

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4. 4. Portfolio Engine Design

Portfolio Engine Design

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4. Example: investment in five assets

Example: investment in five assets

o A global equity portfolio • Invested in 5 equity markets: AU, US, UK, JP and EM • Investment returns accounted using AU Dollar(home currency) currency). • 10 years investment period with rebalancing annually.

• 50 bps proportional transaction cost rate charged on absolute50 bps proportional transaction cost rate charged on absolute turnover of the portfolio at every portfolio rebalancing time. • Investors might have different risk preferences.

o Objective: find optimal strategy to maximise the total expected utility function for the investor.

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4. Result: multi

Result: multi‐‐period

period vs

vs CAPM

CAPM

Blue line interpolated efficient

Blue line: interpolated efficient frontier of a CAPM style

investment

Red line: multi‐period optimization

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4. Example: Visualization of Dynamic

Example: Visualization of Dynamic

Decisions

• Dynamic solution display through motion plots; • Interactive for decision makers; • Intuitive illustration of future investment decisions in an t i i t uncertain environment. Risk Analytics, Real‐Options and Optimal Decisions CSIRO

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4. Example: hedge inflation for post

4. Example: hedge inflation for post‐‐

i

h

i

h

retirement phase

o An post retirement client: o An post‐retirement client:

• Invested in 2 equity markets: domestic & international; • A dynamic withdraw pattern subject to CPI;A dynamic withdraw pattern subject to CPI;

• Some income protection products to hedge the risks, for example, an CPI linked annuity product.

o Objective: find optimal strategy to maximise the total expected j p gy p utility function for the investor.

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4. 4. Dynamic Portfolio Decisions

Dynamic Portfolio Decisions

Simulation scenarios: Optimal strategies:

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Deliverables

1. 1. Prototype quantitative models

Prototype quantitative models

2 2 P bli

P bli

ti

2. 2. Publications

Publications

o

o ATO Data AnalysisATO Data Analysis

Si l ti f U t i t f P i A l i (SUPA) Si l ti f U t i t f P i A l i (SUPA) o

o Simulation of Uncertainty for Pension Analysis (SUPA)Simulation of Uncertainty for Pension Analysis (SUPA) o

o New Pricing Algorithms for Innovative Guaranteed Investment New Pricing Algorithms for Innovative Guaranteed Investment Products

Products o

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Publications

White papersp p Zili Zhu and Thomas Sneddon: The impact on superannuation fund balances from the new compulsory superannuation CSIRO Digital Flagship, CSIRO e‐Publish: EP147667, 11 September 2014. Journal papersp p •Thomas Sneddon, Zili Zhu and Colin O’Hare (2014).Methodology of modelling retirement outcomes. Preprint. Submitted to Mathematical Population Studies: An International Journal of Mathematical Demography

•Xiaolin Luo and PV Shevchenko (2014) Fast Numerical Method for Pricing of Variable Annuities with GuaranteedXiaolin Luo, and P.V. Shevchenko (2014). Fast Numerical Method for Pricing of Variable Annuities with Guaranteed Minimum Withdrawal Benefit under Optimal Withdrawal Strategy. Preprint. Submitted to Risks •Xiaolin Luo, and P.V. Shevchenko (2014). Valuation of Variable Annuities with Guaranteed Minimum Withdrawal and Death Benefits via Stochastic Control Optimization. Preprint. Submitted to Insurance: Mathematics and E i Economics. Technical reports •P. Shevchenko and Xiaolin Luo (2014). Pricing Variable Annuities Under the Optimal Withdrawal Strategy using ( ) g p gy g Gauss‐Hermite Quadrature on a Cubic Spline Interpolation. CSIRO technical report EP 143816.

•P. Shevchenko and Xiaolin Luo (2013). Valuation of variable Annuities with Guaranteed Minimum Withdrawal Benefits via Finite Difference Method. CSIRO technical report EP 1312048. Thomas Sneddon, Zili Zhu and , Colin O’Hare (2014). The SUPA (Simulation of Uncertainty for Pension Analysis) Model: Technical Report. CSIRO technical report. Thomas Sneddon, Zili Zhu and Colin O’Hare (2014). Applications of the SUPA Model: Technical Report. CSIRO technical report technical report. Risk Analytics, Real‐Options and Optimal Decisions CSIRO