A UNIVERSAL OPTIMAL CONSUMPTION RATE FOR AN INSIDER | Zendy

Øksendal Bernt | Zendy

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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.

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