Miklós Rásonyi

No-arbitrage criteria for financial markets with efficient friction

Abstract. We consider a multi-asset discrete-time model of a financial market with proportional transaction costs and efficient friction and prove necessary and sufficient conditions for the absence of arbitrage. Our main result is an extension of the Dalang–Morton–Willinger theorem. As an application, we establish a hedging theorem giving a description of the set of initial endowments which allows to super-replicate a given contingent claim.

On the closedness of sums of convex cones in \(L^0\) and the robust no-arbitrage property

Abstract. This note is a natural complement to our previous work where we studied no-arbitrage criteria for markets with efficient friction. We discuss, in our general geometric framework, the recent result of Walter Schachermayer on a necessary and sufficient condition for the existence of strictly consistent price systems and give its quick proof.

The Fundamental Theorem of Asset Pricing Under Transaction Costs

This paper proves the fundamental theorem of asset pricing with transaction costs, when bid and ask prices follow locally bounded càdlàg (right-continuous, left-limited) processes.The robust no free lunch with vanishing risk condition (RNFLVR) for simple strategies is equivalent to the existence of a strictly consistent price system (SCPS). This result relies on a new notion of admissibility, which reflects future liquidation opportunities. The RNFLVR condition implies that admissible strategies are predictable processes of finite variation.The Appendix develops an extension of the familiar Stieltjes integral for càdlàg integrands and finite-variation integrators, which is central to modelling transaction costs with discontinuous prices.

ON UTILITY MAXIMIZATION IN DISCRETE-TIME FINANCIAL MARKET MODELS

We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are constructed using optimal strategies.

On Optimal Investment for a Behavioral Investor in Multiperiod Incomplete Market Models

We provide easily verifiable conditions for the well-posedness of the optimal investment problem for a behavioral investor in an incomplete discrete-time multiperiod financial market model, for the first time in the literature. Under two different sets of assumptions we also establish the existence of optimal strategies.

Arbitrage Under Transaction Costs Revisited

We present a novel arbitrage-related notion for markets with transaction costs in discrete time and characterize it in terms of price systems. Pertinence of this concept is demonstrated. A discussion of the case with one risky asset and an outlook on continuous-time models complement the main result.

Hedging, Arbitrage, and Optimality with Superlinear Frictions

In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices arbitrarily unfavorable for high trading intensity. Such frictions induce a duality between feasible trading strategies and shadow execution prices with a martingale measure. Utility maximizing strategies exist even if arbitrage is present, because it is not scalable at will.

Fragility of arbitrage and bubbles in local martingale diffusion models

For any positive diffusion with minimal regularity, there exists a semimartingale with uniformly close paths that is a martingale under an equivalent probability. As a result, in models of asset prices based on such diffusions, arbitrage and bubbles alike disappear under proportional transaction costs or under small model mis-specifications. Thus, local martingale diffusion models of arbitrage and bubbles are not robust to small trading and monitoring frictions.

New methods in the arbitrage theory of financial markets with transaction costs

Using entirely new methods, we reprove the main result of [6]: strict absence of arbitrage is equivalent to the existence of a strictly consistent price system in markets with efficient proportional transaction costs in finite discrete time. We also improve on that result by considering a more general class of models.

Convergence of Utility Indifference Prices to the Superreplication Price

A discrete-time financial market model is considered with a sequence of investors whose preferences are described by concave strictly increasing functions defined on the positive axis. Under suitable conditions, we show that the utility indifference prices of a bounded contingent claim converge to its superreplication price when the investors’ absolute risk-aversion tends to infinity.