A UNIVERSAL OPTIMAL CONSUMPTION RATE FOR AN INSIDER

³e 0´(t) e 0 ¼, A, ¸c(t) e 0 (c)X (t)We consider a cash flow modeled by the stochastic equationwhere B(·) and are a Brownian motion and a Poissonian random measure, respectively, and is the consumption/dividend rate. No assumptions are made on adaptedness of the coefficients , and c, and the (possibly anticipating) integrals are interpreted in the forward integral sense. We solve the problem to find the consumption rate c(·), which maximizes the expected discounted utility given byHere is a given measurable stochastic process representing a discounting exponent and A is a random time with values in (0, ), representing a terminal/default time, while is a known constant.X (t)(c) c(t) e 0¼, A, ¸ ´(t) e 0³e 0