In this paper we study the expected utility maximization problem for discretetime incomplete financial markets. As shown by Xia and Yan (2000a, 2000b) in the continuous-time case, this problem can be solved by the martingale measure method. In a special discrete-time model, we explicitly work...

In this paper, we introduce a numeraire-free and original probability based framework for financial markets. We reformulate or characterize fair markets, the optional decomposition theorem, superhedging, attainable claims and complete markets in terms of martingale deflators, present a recent...

It is shown that in a market modeled by a vector-valued semimartingale, when we choose the wealth process of an admissible self-financing strategy as a numeraire such that the historical probability measure becomes a martingale measure, then this numeraire must be the wealth process of a growth...

Since Markowitz published his seminal work on mean-variance portfolio selection in 1952, almost all literature in the past half century adhere their investigation to a binding budget spending assumption on this classical investment issue. In the mean-variance world for a market of all risky...

We provide conditions on a one-period-two-date pure exchange economy with rank-dependent utility agents under which Arrow-Debreu equilibria exist. When such an equilibrium exists, we derive the state-price density explicitly, which is a weighted marginal rate of substitution between the initial...

In this paper we develop a set of axioms for preferences under uncertainty which leads to a representation result unifying the Choquet expected utility preferences of Schmeidler (1989) and the uncertainty averse preferences of Cerreia-Vioglio et al (2011). The maxmin Choquet expected utility, as...

We study Arrow-Debreu equilibria for a one-period-two-date pure exchange economy with rank-dependent utility agents having heterogeneous probability weighting and outcome utility functions. In particular, we allow the economy to have a mix of expected utility agents and rank-dependent utility...

This paper investigates monotone solutions of the moral hazard problems without the monotone likelihood ratio property. The optimal monotone solutions are explicitly characterized by a concave envelope relaxation approach for a two-action model in which the principal is risk neutral or exhibits...

The results on the mean-variance hedging problem in Gouri\'eroux, Laurent and Pham (1998), Rheinl\"ander and Schweizer (1997) and Arai (2005) are extended to discontinuous semimartingale models. When the num\'eraire method is used, we only assume the Radon-Nikodym derivative of the...

The comparative statics of the optimal portfolios across individuals is carried out for a continuous-time complete market model, where the risky assets price process follows a joint geometric Brownian motion with time-dependent and deterministic coefficients. It turns out that the indirect...