A UNIVERSAL OPTIMAL CONSUMPTION RATE FOR AN INSIDER

Abstract

We consider a cash flow X ( c ) ( t ) modeled by the stochastic equation image where B (·) and are a Brownian motion and a Poissonian random measure, respectively, and c ( t ) ≥ 0 is the consumption/dividend rate. No assumptions are made on adaptedness of the coefficients μ, σ, θ , 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 by image Here δ( t ) ≥ 0 is a given measurable stochastic process representing a discounting exponent and τ is a random time with values in (0, ∞), representing a terminal/default time, while γ≥ 0 is a known constant.