Journal ArticleDOI
A solution approach to valuation with unhedgeable risks
TLDR
A class of stochastic optimization models of expected utility in markets with stochastically changing investment opportunities is studied, which expresses the value function in terms of the solution of a linear parabolic equation, with the power exponent depending only on the coefficients of correlation and risk aversion.Abstract:
We study a class of stochastic optimization models of expected utility in markets with stochastically changing investment opportunities. The prices of the primitive assets are modelled as diffusion processes whose coefficients evolve according to correlated diffusion factors. Under certain assumptions on the individual preferences, we are able to produce reduced form solutions. Employing a power transformation, we express the value function in terms of the solution of a linear parabolic equation, with the power exponent depending only on the coefficients of correlation and risk aversion. This reduction facilitates considerably the study of the value function and the characterization of the optimal hedging demand. The new results demonstrate an interesting connection with valuation techniques using stochastic differential utilities and also, with distorted measures in a dynamic setting.read more
Citations
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Book ChapterDOI
Stochastic Differential Equations
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Journal ArticleDOI
An example of indifference prices under exponential preferences
TL;DR: This analysis is based on an explicitly solved example of a European claim written on a nontraded asset, in a model where risk preferences are exponential, and the traded and nontrading asset are diffusion processes with lognormal and arbitrary dynamics.
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Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives
TL;DR: In this paper, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets, and present and analyze multiscale stochastically volatility models and asymptotic approximations.
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Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE
TL;DR: In this paper, the authors propose a method for solving control problems by verification, which is based on the Viscosity Solution Equation (VSP) in the sense of VVS.
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Valuation of Claims on Nontraded Assets Using Utility Maximization
TL;DR: In this article, a second nontraded log Brownian asset is introduced into the Merton investment model with power law and exponential utilities, and a series approximation to the optimal hedge and reservation price using the power utility is obtained.
References
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Stochastic Differential Equations
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Controlled Markov processes and viscosity solutions
Wendell H. Fleming,H. Mete Soner +1 more
TL;DR: In this paper, an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions is given, as well as a concise introduction to two-controller, zero-sum differential games.
Book ChapterDOI
Optimum Consumption and Portfolio Rules in a Continuous-Time Model*
TL;DR: In this paper, the authors considered the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the geometric Brownian motion hypothesis, which implies that asset prices are stationary and lognormally distributed.