Name
Title | ||
|---|---|---|
Forward---Backward Stochastic Differential Games and Stochastic Control under Model Uncertainty |
Abstract | ||
|---|---|---|
We study optimal stochastic control problems with jumps under model uncertainty. We rewrite such problems as stochastic differential games of forward---backward stochastic differential equations. We prove general stochastic maximum principles for such games, both in the zero-sum case (finding conditions for saddle points) and for the nonzero sum games (finding conditions for Nash equilibria). We then apply these results to study robust optimal portfolio-consumption problems with penalty. We establish a connection between market viability under model uncertainty and equivalent martingale measures. In the case with entropic penalty, we prove a general reduction theorem, stating that a optimal portfolio-consumption problem under model uncertainty can be reduced to a classical portfolio-consumption problem under model certainty, with a change in the utility function, and we relate this to risk sensitive control. In particular, this result shows that model uncertainty increases the Arrow---Pratt risk aversion index. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/s10957-012-0166-7 | Journal of Optimization Theory and Applications |
Keywords | Field | DocType |
model uncertainty,maximum principle,robust control,optimal portfolio,forward---backward sdes,optimal consumption,jump diffusions,stochastic differential games,viability | Mathematical optimization,Martingale (probability theory),Maximum principle,Stochastic differential equation,Stochastic modelling,Risk aversion,Nash equilibrium,Robust control,Mathematics,Stochastic control | Journal |
Volume | Issue | ISSN |
161 | 1 | 1573-2878 |
Citations | PageRank | References |
8 | 0.73 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernt Oksendal | 1 | 89 | 15.84 |
| Agnès Sulem | 2 | 98 | 20.64 |