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Stochastic Depreciation and Optimal Consumption‐Investment Decisions

Huw Rhys and Mark Tippet

Journal of Business Finance & Accounting, 2002, vol. 29, issue 1‐2, 273-286

Abstract: Capital accumulation is viewed as the net outcome of accumulation and wasting. Accumulation is modelled by a Gaussian process whilst wasting is generated by a continuous time and continuous state‐space pseudo‐Poisson process. These assumptions imply that an economic agent’s preferences, consumption, capital accumulation and wastage are governed by a form of Hamilton‐Jacobi‐Bellman equation containing an infinite number of terms. We demonstrate the optimisation procedures applicable to consumption and the expected wastage of capital and in the process show that isoelastic preferences are consistent with the model.

Date: 2002
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