The article examines the problem of determining asset allocation to sustainable retirement portfolio. The article attempts to apply heuristic method – 100 minus age in stocks rule – to determine asset allocation to sustainable retirement portfolio. Using dynamic stochastic simulation and stochastic optimization techniques the optimization of heuristic method rule is presented and the optimal alternative to „100“ is found. Seeking to reflect the stochastic nature of stock and bond returns and the human lifespan, the dynamic stochastic simulation models incorporate both the stochastic returns and the probability of living another year based on Lithuania‘s population mortality tables. The article presents the new method – adjusted heuristic method – to be used to determine asset allocation to retirement portfolio and highlights its advantages.
AbstractWe propose and analyse a method based on the Riccati transformation for solving the evolutionary Hamilton–Jacobi–Bellman equation arising from the dynamic stochastic optimal allocation problem. We show how the fully nonlinear Hamilton–Jacobi–Bellman equation can be transformed into a quasilinear parabolic equation whose diffusion function is obtained as the value function of a certain parametric convex optimization problem. Although the diffusion function need not be sufficiently smooth, we are able to prove existence and uniqueness and derive useful bounds of classical Hölder smooth solutions. Furthermore, we 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 travelling 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 the application of the method.
A Dynamic Stochastic Network Model of the Unsecured Interbank Lending Market
