Stochastic Volatility Modeling

Local volatility 95

is preferable to go back to square one and cast the delta-hedging strategy as a

stochastic control problem that maximizes a utility function which balances

the costs generated by hedging with the benet of a reduced uncertainty of

our nal P&L. This was done by Mark Davis, Vassilios Panas and Thaleia

Zhariphopoulou in [

35

]. In practice, an exponential utility function

e

−λP &L

is

well suited as the ensuing delta strategy is independent on the initial wealth.

31

31

Solving this stochastic control problem numerically is tricky, as its solution is of the bang-bang

type. The optimal hedging strategy is a function of

t, S

and the current delta: ...