4 research outputs found
Expected Utility Maximization and Conditional Value-at-Risk Deviation-based Sharpe Ratio in Dynamic Stochastic Portfolio Optimization
In this paper we investigate the expected terminal utility maximization
approach for a dynamic stochastic portfolio optimization problem. We solve it
numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which
is transformed by means of the Riccati transformation. We examine the
dependence of the results on the shape of a chosen utility function in regard
to the associated risk aversion level. We define the
Conditional value-at-risk deviation () based Sharpe ratio for
measuring risk-adjusted performance of a dynamic portfolio. We compute optimal
strategies for a portfolio investment problem motivated by the German DAX 30
Index and we evaluate and analyze the dependence of the -based Sharpe
ratio on the utility function and the associated risk aversion level
Transformation Method for Solving Hamilton-Jacobi-Bellman Equation for Constrained Dynamic Stochastic Optimal Allocation Problem
In this paper we propose and analyze a method based on the Riccati
transformation for solving the evolutionary Hamilton-Jacobi-Bellman equation
arising from the stochastic dynamic optimal allocation problem. We show how the
fully nonlinear Hamilton-Jacobi-Bellman equation can be transformed into a
quasi-linear parabolic equation whose diffusion function is obtained as the
value function of certain parametric convex optimization problem. Although the
diffusion function need not be sufficiently smooth, we are able to prove
existence, uniqueness and derive useful bounds of classical H\"older smooth
solutions. We furthermore construct a fully implicit iterative numerical scheme
based on finite volume approximation of the governing equation. A numerical
solution is compared to a semi-explicit traveling wave solution by means of the
convergence ratio of the method. We compute optimal strategies for a portfolio
investment problem motivated by the German DAX 30 Index as an example of
application of the method
A transformation method for solving Hamilton-Jacobi-Bellman equation for constrained dynamic stochastic optimal allocation problem
In this paper we propose and analyze a method based on the Riccati transformation for solving the evolutionary Hamilton-Jacobi-Bellman equation arising from the stochastic dynamic optimal allocation problem. We show how the fully nonlinear Hamilton-Jacobi-Bellman equation can be transformed into a quasi-linear parabolic equation whose diffusion function is obtained as the value function of certain parametric convex optimization problem. Although the diffusion function need not be sufficiently smooth, we are able to prove existence, uniqueness and derive useful bounds of classical H\"older smooth solutions. We furthermore construct a fully implicit iterative numerical scheme based on finite volume approximation of the governing equation. A numerical solution is compared to a semi-explicit traveling wave solution by means of the convergence ratio of the method. We compute optimal strategies for a portfolio investment problem motivated by the German DAX 30 Index as an example of application of the method.
doi:10.1017/S144618111300031