Abstract This paper introduces optimal expected utility (OEU) risk measures, investigates their main properties and puts them in perspective to alternative risk measures and notions of certainty equivalents. By taking the investor’s point of view, OEU maximizes the sum of capital available...

We consider a continuous time Markov switching model (MSM) which is widely used in mathematical finance. The aim is to estimate the parameters given observations in discrete time. Since there is no finite dimensional filter for estimating the underlying state of the MSM, it is not possible to...

In a market with partial information we consider the optimal selection of portfolios for utility maximizing investors under joint budget and shortfall risk constraints. The shortfall risk is measured in terms of expected loss. Stock returns satisfy a stochastic differential equation. Under...

In a discrete-time incomplete financial market with proportional transaction costs and with independent and bounded returns, we prove the existence of a consistent price system that can be written as the expectation of the discounted claim under the real-world probability measure P and not just...

In a market with partial information we consider the optimal selection of portfolios for utility maximizing investors under joint budget and shortfall risk constraints. The shortfall risk is measured in terms of expected loss. Stock returns satisfy a stochastic differential equation. Under...

In the CRR model we introduce a transaction cost structure which covers piecewise proportional, fixed and constant costs. For a general utility function we formulate the problem of maximizing the expected utility of terminal wealth as a Markov control problem. An existence result is given and...

Portfolio optimization problems on a finite time horizon under proportional transaction costs are considered. The objective is to maximize the expected utility of the terminal wealth. The ensuing non-smooth time-dependent Hamilton–Jacobi–Bellman equation is solved by regularization and the...

<Para ID="Par1">The aim of this paper is to prove the fundamental theorem of asset pricing (FTAP) in finite discrete time with proportional transaction costs by utility maximization. The idea goes back to L.C.G. Rogers’ proof of the classical FTAP for a model without transaction costs. We consider one risky...</para>