Risk-Sensitive ICAPM With Application to Fixed-Income Management

Abstract

This paper presents an application of risk-sensitive control theory in financial decision making. A variation of Merton's continuous-time intertemporal capital asset pricing model is developed where the infinite horizon objective is to maximize the portfolio's risk adjusted growth rate. The resulting model is tractable and thus provides economic insight about optimal trading strategies as well as the fact that the strategy of 100% cash is not necessarily the least risky one. For fixed-income applications we utilize the concept of rolling-horizon bonds, which are stochastic process models of certain mutual funds of zero coupon bonds. We show by numerical example that the optimal proportion of one's wealth to hold in an asset is given by a simple affine function of economic factors such as interest rates of various maturities.Index Terms-Fixed-income management, intertemporal capital asset pricing model, optimal portfolios, risk-sensitive control.

Optimal Investment Decisions for a Portfolio With a Rolling Horizon Bond and a Discount Bond

“…Moreover, it follows directly and immediately from Rutkowski [16] (see also [2]) that σ = −T D T e 2 . In view of (2.7) we thus have…”

“…For a justification of the dynamics for S 1 (·), see section 5 in Bielecki-Pliska [2]. A discussion of the dynamics for S 2 (·) is provided in Sec.…”

Long-term optimal portfolios with floor

“…4. Also, refer to Bielecki and Pliska [3,4], Davis and Lleo [8], Fleming and Sheu [12,13], Hata and Iida [20], Kuroda and Nagai [29], Nagai [34], Nagai and Peng [36] and Sekine [45], for example. (ii) (RS) with the drawdown constraint, i.e.,…”

“…Define now the risky asset price process S by (2.1), (3.8) and (3.9). This incomplete market model is employed and analyzed in [45] and similar models are treated in [3,4,8,12,13,29], for example. Assume here that r 2 is symmetric and r 2 ≥ 0, σ σ > 0, aa > 0, and b 1 is stable (3.10) and that |γ | is sufficiently small.…”

A note on long-term optimal portfolios under drawdown constraints

“…is included in risk-sensitive-type portfolio optimization problems, which have been studied by several authors by analysing the associated Bellman equations with Markovian models; see [2], [12], [16], and the references therein, for example. We note that there are different difficulties in the analyses of the respective situations in which γ < 0 and γ > 0.…”