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...

<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>

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 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...

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...

In this paper, we deal with the pricing of European options in an incomplete market. We use the common risk measures Value-at-Risk and Expected Shortfall to define good-deals on a financial market with log-normally distributed rate of returns. We show that the pricing bounds obtained from the...