Robust portfolio selection under exponential preferences
Tom 37 / 2010
Applicationes Mathematicae 37 (2010), 215-230
MSC: 91G10, 91A15, 91A23, 49L99, 93E20.
DOI: 10.4064/am37-2-6
Streszczenie
We consider an incomplete market with an untradable stochastic factor and a robust investment problem based on the CARA utility. We formulate it as a stochastic differential game problem, and use Hamilton–Jacobi–Bellman–Isaacs equations to derive an explicit representation of the robust optimal portfolio; the HJBI equation is transformed using a substitution of the Cole–Hopf type. Not only the pure investment problem, but also a problem of robust hedging is taken into account: an agent tries to hedge the risk associated with derivatives based on the stochastic factor.
