LisMath Seminar 

21/04/2022, 14:00 — 14:30 — Online
Paulo Rocha, Faculdade de Ciências, Universidade de Lisboa

Dynamic Programming and the Portfolio Problem with Consumption (Under the $\alpha$-Hypergeometric Stochastic Volatility Model)

The portfolio problem for a stochastic volatility model goes way back to Merton in his seminal paper "Lifetime Portfolio Selection under Uncertainty: the Continuous-Time Case" [1].

In this seminar we will look at the dynamic programming method to solve a variant of the portfolio problem in which consumption is allowed. We assume that the agent makes his investment and consumption decisions based on a power utility function.

Considering a simple portfolio, composed by a bond and a single stock on a market modelled by the $\alpha$-Hypergeometric Stochastic volatility model, we will derive the correspondent Hamilton-Jacobi-Bellman equation and discuss the existence of a classical solution and the techniques used to find such solution.

References:

[1] Merton R.C. “Lifetime Portfolio Selection under Uncertainty: the Continuous-Time Case,” The Review of Economics and Statistics, 51, No. 3, 247–257 (1969).