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A UNIVERSAL OPTIMAL CONSUMPTION RATE FOR AN INSIDER
Author(s) -
Øksendal Bernt
Publication year - 2006
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2006.00264.x
Subject(s) - brownian motion , terminal value , discounting , mathematics , cash flow , consumption (sociology) , measure (data warehouse) , stochastic discount factor , hyperbolic discounting , econometrics , geometric brownian motion , mathematical economics , economics , diffusion process , computer science , statistics , finance , capital asset pricing model , social science , database , sociology , cash management , economy , service (business)
We consider a cash flow X ( c ) ( t ) modeled by the stochastic equationwhere 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 byHere 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.