Optimal Hedging for Fund Insurance Managers with Partially Observable Investment Flows

摘要

All the financial practitioners are working in incomplete markets full ofunhedgeable risk-factors. Making the situation worse, they are only equippedwith the imperfect information on the relevant processes. In addition to themarket risk, fund and insurance managers have to be prepared for sudden andpossibly contagious changes in the investment flows from their clients so thatthey can avoid the over- as well as under-hedging. In this work, the prices ofsecurities, the occurrences of insured events and (possibly a network of) theinvestment flows are used to infer their drifts and intensities by a stochasticfiltering technique. We utilize the inferred information to provide the optimalhedging strategy based on the mean-variance (or quadratic) risk criterion. ABSDE approach allows a systematic derivation of the optimal strategy, which isshown to be implementable by a set of simple ODEs and the standard Monte Carlosimulation. The presented framework may also be useful for manufactures andenergy firms to install an efficient overlay of dynamic hedging by financialderivatives to minimize the costs.