We calculate explicitly the optimal strategy for an investor with exponential utility function when the price of a single risky asset (stock) follows a discrete-time autoregressive Gaussian process. We also calculate its performance and analyse it when the trading horizon tends to infinity. Dependence of the asymptotic performance on the autoregression parameter is determined. This provides, to the best of our knowledge, the first instance of a theorem linking directly the memory of the asset price...
The following question is due to Marc Yor: Let be a brownian motion and
=+
. Can we define an -predictable process such that the resulting stochastic integral (⋅) is a brownian motion (without drift) in its own filtration, i.e. an -brownian motion? In this paper we show that by dropping the requirement of -predictability of we can give a positive answer to this question. In other words, we are able to show that there is a weak solution to Yor’s question. The original...
We consider a discrete-time, generically incomplete market model and a behavioural investor with power-like utility and distortion functions. The existence of optimal strategies in this setting has been shown in Carassus-Rásonyi (2015) under certain conditions on the parameters of these power functions.
In the present paper we prove the existence of optimal strategies under a different set of conditions on the parameters, identical to the ones in Rásonyi-Rodrigues (2013), which...
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