Name
Abstract | ||
|---|---|---|
We consider a market model with one risk-free and one risky asset, in which the dynamics of the risky asset are governed by a geometric Brownian motion. In this market we consider an investor who consumes from the bank account and who has the opportunity at any time to transfer funds between the two assets. We suppose that these transfers involve a fixed transaction cost k0, independent of the size of the transaction, plus a cost proportional to the size of the transaction.The objective is to maximize the cumulative expected utility of consumption over a planning horizon. We formulate this problem as a combined stochastic control/impulse control problem, which in turn leads to a (nonlinear) quasi-variational Hamilton--Jacobi--Bellman inequality (QVHJBI). We prove that the value function is the unique viscosity solution of this QVHJBI. Finally, numerical results are presented. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1137/S0363012900376013 | Siam Journal on Control and Optimization |
Keywords | Field | DocType |
risky asset,bank account,optimal consumption,combined stochastic control,fixed transaction cost k0,numerical result,geometric brownian motion,market model,impulse control problem,cumulative expected utility,proportional transaction costs,bellman inequality,transaction cost | Transaction cost,Mathematical optimization,Time horizon,Expected utility hypothesis,Bellman equation,Portfolio,Database transaction,Mathematics,Geometric Brownian motion,Stochastic control | Journal |
Volume | Issue | ISSN |
40 | 6 | 0363-0129 |
Citations | PageRank | References |
27 | 3.30 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernt Oksendal | 1 | 89 | 15.84 |
| Agnès Sulem | 2 | 98 | 20.64 |