Consumption and Portfolio Selection

Ser-Huang Poon

Chapter 4 in Advanced Finance Theories, 2018, pp 39-63 from World Scientific Publishing Co. Pte. Ltd.

Abstract: This chapter follows closely the materials in Merton (1990, Chapter 4). Section 4.1 first presents a simple single-period portfolio selection problem and shows how the solution is simplified when there is a risk free rate for lending and borrowing. The context is then extended to multiperiod where the focus is on the asset allocation decision between risk free and risky assets and all individuals have finite life span. In this case, the asset allocation decision has to be solved via dynamic programming based on the Hamilton–Jacobi– Bellman equation. If we relax the assumption to infinite horizon, for example by taking the position of a pension fund that never liquidates, then analytical solutions are possible. It is under this special setting that we solve the optimal asset allocation decision and obtain the optimal portfolio for individuals with three different types of utility functions, viz. constant relative risk aversion (CRRA), constant absolute risk aversion (CARA) and hyperbolic absolute risk aversion (HARA). In this chapter, we omit the discussion on the bequest valuation function.

Keywords: Intertemporal Portfolio Selection; Capital Structure; General Equilibrium; Spanning; Mutual Fund Theorem; Jumps; Incomplete Markets (search for similar items in EconPapers)
JEL-codes: G30 (search for similar items in EconPapers)
Date: 2018
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