Options traded on financial assets allow market partic- ipants to take views on the future values of the assets themselves. This projection towards the future confers to the option a sort of forward-looking information on the future evolution of the underlying assets. For example, in the case of Call option, the larger today’s premium is, the higher is the probability to exert the option and greater is the likelihood that the asset price finishes above the strike price at maturity. These probabilities, taken together, form the so-called implied Probability Density Function also referred as Risk NeutralDensity function (henceforth RND). More precisely, when the market operators eval- uate theoretically an option price, they formulate their own estimates of these probabilities and their ’feelings’ about future evolutions of the underlying asset are sum- marized in the RND. The reason why it is called ’Risk Neutral’ density is that because it is estimated in a risk neutral world (in opposition with the real world) under which all investors are assumed to have no risk prefer- ences. A relatively large number of estimation methods has been proposed in the empirical literature and almost all are based on one of the following approaches:
and (13) is equivalent to satisfying inequality (6) (passing the critical popu- lation size). Thus at the stationary size manifold the threshold between the growth and decline of the strategy frequency is equivalent to the threshold between the growth and decline of the number of carriers of that strategy (this may not be satisfied far from the stationary size manifold). Frequency dependence induces an increase of the slope of the threshold which eventu- ally leads to the selection of the strategy with the greatest L, which confirms the result of Mylius and Diekmann (1995). Note that their second result, that density dependent adult mortality leads simply to r maximization as in unlimited growth models, directly comes from the independence of the replicator dynamics from background fitness.
Two strategies to impose the nonnegativity of the RNPM are presented and discussed in this paper. The first and simpler strategy is to require the estimated pdf to remain nonnegative at the spline nodes. This scheme maintains the QP structure of the problem since it brings only linear inequal- ity constraints to the basic formulation. However, there is no guarantee of nonnegativity between the spline nodes. Our second approach replaces the basic QP formulation with a semidefinite programming (SDP) formulation but rigorously ensures the nonnegativity of the estimated pdf in its entire domain. It is based on an SDP characterization of nonnegative polynomial functions due to Bertsimas and Popescu  and requires additional vari- ables and linear equality constraints as well as semidefiniteness constraints on some matrix variables. To our knowledge, this is the first spline function approach to risk-neutraldensity estimation with a positivity guarantee.
This paper explores the dynamics of risk aversion of a representative agent with an iso-elastic utility function. In contrast to most of the existing litera- ture, we estimate the coefficient of relative risk aversion from option prices. To do this, we transform the risk-neutraldensity function obtained from a cross-section of option prices to an objective distribution function that re- flects individuals’ risk aversion through a CRRA utility function. The dynam- ics of the relative risk-aversion coefficient are obtained by repeating the same estimation procedure over rolling windows. This procedure uncovers strong variation in risk aversion over time. We also propose a simulation procedure to construct confidence intervals for the risk-aversion coefficient in each pe- riod. We assess the robustness of these confidence intervals under different assumptions on the data generating process of stock prices. The results imply a strong influence of volatility on the variation of risk aversion. In an empiri- cal application, we compare the forecasting performance of our approach based on our risk-aversion estimates against the method proposed in . Overall, we find that our simulation based approach obtains better forecast- ing results than bootstrap methods.
There are some other schemes to form the FRC with- out large power input within a short period. A rotating magnetic field (RMF) is a major candidate to drive steady plasma current in the FRC and is also capable of generat- ing the FRC equilibrium. Many numerical [2–7] and ex- perimental studies [8–13] have been conducted, and long- pulse  or high-performance  plasmas have been achieved recently. Long-term FRC sustainment requires particle supply as well as power input from the RMF; therefore, a certain amount of neutral particle density (hereafter abbreviated as neutraldensity) is considered to be essential for steady-state sustainment. A considerably high neutraldensity, which leads to suppression of the ion spin-up due to electron drag [3, 7], is usually employed in numerical studies [2, 4]. On the other hand, a high neutral
Spline functions are piecewise polynomial functions that assume a pre- determined value at certain points (knots) and satisfy certain smoothness properties. Other authors have also used spline fitting techniques in the context of risk-neutraldensity estimation, see [1, 8]. In contrast to existing techniques, we allow the displacement of spline knots in a superset of the set of points corresponding to option strikes. The additional set of knots makes our model flexible and we use this flexibility to optimize the fit of the spline function to the observed prices. The basic formulation, without requiring the nonnegativity of the risk-neutral probability density function (pdf), is a convex quadratic programming (QP) problem.
difficult, if not impossible, to achieve. The attempt to reduce the information bias and use infor- mation sets as complete as possible in the estimation process of both densities is the starting point of this research. In general, while the risk neutraldensity is well extracted from option data, the estimation of the conditional physical density is often rather imprecise 34 . To date, the majority of models rely on past returns/prices, which do not include a significant portion of the (required) in- formation based on which the physical density should be extracted . Compared to historical data, derivative securities are more informative about the underlying asset dynamics (Bollerslev and Todorov (2011)), as they naturally embed investors’ expectations about future market scenar- ios. As a consequence, the combined use of derivative and historical data as inputs in the physical density estimation enables one to obtain an information set closer to the one theoretically required. To date, few authors have tried to solve the information bias arising in the PK estimation. Among them, Ross (2015) with the Recovery Theorem has proposed a methodology to directly extract the physical density from the risk neutral one. However, this approach requires the transition- independence of the PK 35 , a condition rarely fulfilled in real world modelling. Recently, Sala et
The temperature values from the MSIS model in the lower thermosphere is based on the assumption that the neu- tral temperature is equal to the ion temperature. The valid- ity of this assumption during the geomagnetically disturbed period can be checked by comparing the rotational tempera- ture with the ion temperature observed by the EISCAT radar during the DELTA campaign. A detailed comparison is pro- vided in Nozawa et al. (2006) in this issue. The EISCAT ion temperature is 200 K higher at and above 120 km than the neutral temperature from the NTV, but the altitude proﬁles are similar. Since the strength of the electric ﬁeld was about 50 mV/m and the agreement is good below 110 km, these authors suggested that the ion/rotational temperature differ- ence above 110 km is caused by Joule heating. They also derived neutral temperatures from the EISCAT ion temper- ature using the steady state ion energy equation and found good agreement for neutral temperatures measured by the NTV and derived by the EISCAT radar observations at and below 110 km. The ion temperature retrieved from inco- herent scatter spectra is inﬂuenced by the ion-neutral col- lision frequency. The ion-neutral collision frequency de- pends on the neutraldensity and composition, so that the large deviation of the observed N 2 number density from the
Γ has two solutions in the R type region, corresponding to a large and a small jump (corresponding to the positive and negative sign in (15)). We call these the weak and strong R type solution. If we assume a density structure that ini- tially evolved through Bondi accretion without ionization, then the solution will naturally evolve into the weak solu- tion with the smallest jump, and this is the solution we will assume below. In this case, the velocity in the ionized re- gion will also be supersonic (see Appendix A for a detailed analysis of weak and strong R type solutions and imposed velocity restrictions).
increases when the density is lowered, but the effect of aug- menting the coupling strength 共or lowering the temperature兲 is more dramatic. Thus, one sees that for the lowest density and highest coupling the number of free ions diminishes con- siderably and neutral clusters 共 especially ion pairs 兲 become dominant. In contrast, at 2 = 0.15, increasing the coupling hardly changes the cluster size distribution. As an illustration of the effect of increasing coupling strength in the low den- sity case, we show in Fig. 7 two snapshots from MC simu- lations in which one can clearly see how free ions practically vanish for ⌫ = 10. Finally, we note in passing that our system is closely related to the 3D restricted primitive model con- fined to a plane, studied by one of us in collaboration with Levesque and Caillol. 39 In this connection, one finds that the cluster size distributions of both systems are very similar. This indicates that the use of a 1 / r or a log r functional
In previous research on SIRENS, both time-integrated and time-resolved measurements have been used to find the temperature and density of a variety of metallic and non-metallic plasmas . A similar study was also performed on the electrothermal plasma device PIPE . These, and other studies performed with the electrothermal devices, used the passive radiation technique of optical (or atomic) emission spectroscopy (OES). This method relies on radiation emitted by the plasma, or particles within the plasma. Other general methods include intrusive techniques and active radiation techniques. The Langmuir, or electrostatic, probe is an example of an intrusive technique. As previously described, this technique was attempted as a way to verify OES measurements, but was unsuitable in this study. Active radiation techniques rely on an external source of radiation as a probe of the plasma so that transmission, absorption, scattering, or reflection measurements can be made. The specialized equipment required made these techniques unsuitable as well .
The two ground-based FPIs at Skibotn (69.3 ◦ N, 20.4 ◦ E) and the Kiruna Esrange Optical Platform System (KEOPS) site (67.8 ◦ N, 20.4 ◦ E) sampled the auroral green line emission at 557.7 nm and provided neutral temperatures and line of site wind velocities. Both FPIs operated a normal scan of cardinal directions plus zenith but the KEOPS FPI had one extra direction of Northwest towards the rocket trajectory as shown in Fig. 1. The detailed description of the instruments and observations is presented by Griffin et al. (2005) in this issue. The neutral temperatures measured from the two directions closest to the sounding rocket, the Skibotn West and the KEOPS Northwest, at the period from 23:00 UT on 12 to 2:00 UT on 13 December 2004 are shown in Fig. 11 of Griffin et al. (2005). The temperatures from two directions are in very good agreement at ∼ 500 K just before the launch time. The Skibotn West data show a temperature jump of 150 K at 0:36:37 UT just after the launch and return to the former 500 K level at the next data point in 7.5 minutes. The KEOPS Northwest temperature gradually increases after the launch time up to ∼ 600 K and drops to ∼ 300 K after 1:15 UT. The data from the other directions show a temperature of around 500 K during the rocket flight. 3.3 Auroral emission height
The backscattering (monostatic) RCS of the plasma coated DB cylinder in comparison with that of dielectric is presented in Fig. 6(a). The backscattering cross-section decreases with increase in operating frequency while it tends to attain a constant value when operating frequency is above 10 GHz. This is obvious as the relative permittivity approaches to unity for such high frequencies. One can observe the unusual surge in monostatic RCS at operating frequencies closer to the plasma frequency. Fig. 6(b) presents a close up analysis of the situation near plasma frequencies. It is observed that for higher electron-neutral collision frequency values, this surge is suppressed as illustrated in Fig. 6(c). It is indicating that the dissipation eﬀects are signiﬁcant for such values of υ , because in this case the imaginary part of permittivity is not zero. An interesting feature is revealed when the physical size of the object is ﬁxed and operating frequencies are varied, as illustrated in Fig. 6(d). The monostatic RCS of the plasma coated cylinder has a linear observed over a range of frequencies while it is in case of a dielectric coating, the object starts oscillating after a certain frequency.
known to be approximately 2.1, 4.4, and 6.6 [55, 56]. Protonation of the dianionic form following the association of Fl-lysozyme with liposomal membranes is likely to be the reason for the observed fluorescence decrease. Notably, according to our estimates obtained in terms of the Gouy-Chapman double-layer theory, the lowest interfacial pH reached at PG content 40 mol% is approximately 5.2 (surface electrostatic potential is -126 mV, ionic strength 20 mM). The monomer binding curves were obtained by monitoring the changes in Fl fluorescence as a function of lipid concentration and membrane content of anionic phospholipids. As seen from Fig. 2A, isotherms of Lz binding to neutral (PC) or weakly charged (PG5 and PG10) model membranes are characterized by a typical hyperbolic shape. Analysis of the obtained curves in terms of scaled particle theory (SPT)-based adsorption models accounting for electrostatic effects revealed that these isotherms can be described by a monomodal model (Eqs. (S1)-(S10) in Supplementary material at http://dx.doi.org/10.2478/s11658- 012-0015-6) which suggests that upon binding to the lipid bilayer the protein retains its native globular conformation and monomeric state. In turn, association of Lz with highly charged lipid vesicles (PG20 and PG40) resulted in the conversion of binding isotherms from hyperbolic to sigmoidal with the steepness of the curves being increased with anionic lipid content (Fig. 2B).
Plasma properties, defined by the magnetic field, electron density, electron temperature and a first estimate for the ion temperature as well as the appropriate lithium beam parameters (energy, beam ion) are entered into ADAS306 which returns LJ-resolved emission coefficients and electron populations for the individual states. These are used as weights for the results of the ADAS603 subroutine, which calculates the line strength of the individual transitions including information about the angle between observation direction and magnetic field line. After weighting, each individual component is assigned the estimated ion temperature and folded with the instrument function. Finally, all com- ponents are summed to form the resulting spectral line. By measuring this complete spectrum in the same way (i.e. by fitting a Gaussian model function) as done with the experimental data, one can calculate an apparent temperature from the ion temperature that enters the model as a guess. By iterating the estimate, any experimental spectrum can be matched with a best guess for the actual ion temperature.