A UNIVERSAL OPTIMAL CONSUMPTION RATE FOR AN INSIDER

Bernt Øksendal

Mathematical Finance, 2006, vol. 16, issue 1, 119-129

Abstract: We consider a cash flow X(c) (t) modeled by the stochastic equation 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 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.

Date: 2006
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