Optimal investment and consumption with stochastic factor and delay
Keywords:stochastic differential delay equation, power utility function, stochastic factor, Cox-Ingersoll-Ross model.
AbstractWe analyse an optimal portfolio and consumption problem with stochastic factor and delay over a finite time horizon. The financial market includes a risk-free asset, a risky asset and a stochastic factor. The price process of the risky asset is modelled as a stochastic differential delay equation whose coefficients vary according to the stochastic factor; the drift also depends on its historical performance. Employing the stochastic dynamic programming approach, we establish the associated Hamiltonâ€“Jacobiâ€“Bellman equation. Then we solve the optimal investment and consumption strategies for the power utility function. We also consider a special case in which the price process of the stochastic factor degenerates into a Coxâ€“Ingersollâ€“Ross model. Finally, the effects of the delay variable on the optimal strategies are discussed and some numerical examples are presented to illustrate the results. doi:10.1017/S1446181119000014
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