Optimal asset allocation for institutional investors/Allocation optimale de portefeuille pour des investisseurs institutionnels
(2003)
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- Abstract
- (en) In this work we contribute to the literature about the optimal asset allocation in continuous-time. In particular, we consider the problem of maximising the expected utility of the investor's final wealth over a finite time horizon. We develop a suitable framework in the dynamic stochastic optimal control theory in order to analyse the optimal asset allocation problem for an institutional investor like a bank, an insurance company, an investment fund, or a pension fund. Such an investor cannot control the contributions to and withdrawals from the managed wealth. In fact, while the classical consumption-portfolio problem considers consumption as a control variable, in our analysis the flows of wealth that are different from the coupons and dividends, are just state variables. We refer to them as "background variables". Furthermore, the analysis explicitly takes into account the inflation risk that is generally neglected by the asset allocation literature. In such a context we present some quasi-explicit solutions for the optimal asset allocation problem without specifying any particular functional form for the drift and diffusion terms of the stochastic differential equations describing the financial market, the background variables, and inflation. The institutional investor's attitude towards risk is supposed to be described by an increasing and concave utility function whose risk aversion is absolutely constant, relatively constant, or hyperbolic according to the problem setting that must be solved. Finally, we explicitly consider the case of a pension fund that must maximise the expected utility of its surplus. Unlike the analyses studying the problem of a non-actuarial institutional investor, the case of a pension fund requires the introduction of two new characteristics: (i) the different behaviour of the fund's wealth during the accumulation and the decumulation phases, and (ii) the mortality risk. We develop a set up aimed at finding out how and how much this mortality risk affects the optimal asset allocation.
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Menoncin, F. (2003). Optimal asset allocation for institutional investors/Allocation optimale de portefeuille pour des investisseurs institutionnels. https://hdl.handle.net/2078.5/41822