Dynamic Hedging with Stochastic Differential Utility

may be deepened further. As a matter of fact, we are able to produce ageneral hedging formula, which nests as special all cases studied in DJ’spaper. Then we specialize it to compare with those obtained by them.As a consequence of regarding prices as Markov processes, the myopichedging problem at each time 1 no longer holds necessarily. Hence, our optimalfutures hedging formulas are not the same as the corresponding statichedges, nor directly comparable to analogous solutions in discrete-time cases,as the results in Anderson and Danthine (1981, 1983).We would like to find some link between both approaches that we havementioned. We do this by making a suitable transformation on the TerminalValue-type utility. Then we take advantage of the compact formulas thatit produces and see explicitly what effect the SDU specification exerts onthe standard model, that is, we introduce the certainty equivalent machineryin the Hamilton-Jacobi-Bellman equation, HJB, of the terminal value utilityand study what effects this causes on the optimal hedge ratio. The particularconcave transformation that we employ is the connection between SDU andTerminal Utility. This adds some degrees of freedom and may potentially improvethe hedging strategy. The main advantage of this specification, hence,is to make DJ’s model a special case, and to allow us to derive interestingand neat results.Our model is similar to DJ in several aspects: spot and futures pricesare vector diffusion processes; a hedge is a vector stochastic process whichspecifies a futures position in each futures market; and the hedging profits1 Myopic hedging at each time means that an agent is hedging only local changes inwealth. Further discussion can be found in Adler and Detemple (1988) and the referencestherein.2