Numerical methods for an optimal investment-comsumption model. (English) Zbl 0744.90003

Fitzpatrick, Ben G.; Fleming, Wendell H.

Math. Oper. Res. 16, No. 4, 823-841 (1991).

Summary: This paper examines some numerical techniques for an investment/consumption problem considered previously by the second author and T. Zariphopoulou [ibid. 16, No. 4, 802-822 (1992; Zbl 0744.90004)]. The value function \(v(x)\) satisfies the differential equation of dynamic programming for \(x>0\). Special monotonicity and concavity features of the problem allow us to prove convergence not only of discrete approximations to \(v(t)\), but of the corresponding discrete approximations to optimal investment and consumption policies.

MSC:

91B28	Finance etc. (MSC2000)
91B62	Economic growth models
49L20	Dynamic programming in optimal control and differential games
93E20	Optimal stochastic control
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

investment/consumption; discrete approximations

Citations:

Zbl 0744.90004