Long run risk sensitive portfolio with general factors

Abstract

In the paper portfolio optimization over long run risk sensitive criterion is considered. It is assumed that economic factors which stimulate asset prices are ergodic but non necessarily uniformly ergodic. Solution to suitable Bellman equation using local span contraction with weighted norms is shown. The form of optimal strategy is presented and examples of market models satisfying imposed assumptions are shown.

Long-Run Risk Sensitive Dyadic Impulse Control

“…Following Sadowy & Stettner (2002) and Pitera & Stettner (2016) we define the Bellman equation for the dyadic impulsive control as…”

“…so that the span ω-norm could be considered as the centered (wrt. 0) ω-norm; see (Pitera & Stettner 2016, Section 3) and (Hairer & Mattingly 2011, Section 2) for details.…”

“…Note that due to Proposition 3.3 we get solution to Bellman equation for any predefined γ < 0. In particular, in contrast to (Pitera & Stettner 2016, Proposition 4), we do not require γ to be close to 0.…”

“…in long-run risk-sensitive portfolio optimisation. As an example, on can easily refine Proposition 5 in Pitera & Stettner (2016) by showing that Bellman equation always corresponds to the optimal strategy (defined therein) without any additional assumptions. This paper is organised as follows.…”

A note on a new class of recursive utilities in Markov decision processes

“…The preferences (1.1) were first studied by Weil [21] and then by Hansen and Sargent [10], who used them to deal with a linear quadratic Gaussian control model. Furthermore, it is worth emphasising that risk sensitive preferences of the form (1.1) have found several applications, for instance, in problems of Pareto optimal allocations [1] or in finance [9,15], where the…”