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We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex duality. The notion of “asymptotic elasticity” of Kramkov and Schachermayer is extended to the time-dependent case. By… (More)

- Gordan Zitkovic
- 2001

We extend the Bipolar Theorem of Brannath and Schachermayer (1999) to the space of nonnegative càdlàg supermartingales on a filtered probability space. We formulate the notion of fork-convexity as an analogue to convexity in this setting. As an intermediate step in the proof of our main result we establish a conditional version of the Bipolar theorem. In an… (More)

This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies – those strategies whose wealth process is… (More)

- Gordan Zitkovic
- 2008

The concept of convex-compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in lieu of compactness in a variety of cases. In particular, we show that bounded-in-probability, convex and closed subsets… (More)

- Gordan Zitkovic
- 2004

We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility-maximization problems including the classical ones of terminal wealth or consumption, as… (More)

- Thaleia Zariphopoulou, Gordan Zitkovic
- SIAM J. Financial Math.
- 2008

The new notion of maturity-independent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion framework, that, surprisingly, some of the widely utilized risk measures cannot be used to build maturity-independent… (More)

- Gordan Zitkovic
- Finance and Stochastics
- 2006

We establish existence of stochastic financial equilibria on filtered spaces more general than the ones generated by finite-dimensional Brownian motions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal constraints. We deal with random endowment density streams which admit jumps and general time-dependent… (More)

- Gordan Zitkovic
- Finance and Stochastics
- 2012

In an incomplete semimartingale model of a financial market, we consider several risk-averse financial agents who negotiate the price of a bundle of contingent claims. Assuming that the agents’ risk preferences are modelled by convex capital requirements, we define and analyze their demand functions and propose a notion of a partial equilibrium price. In… (More)

We consider two risk-averse financial agents who negotiate the price of an illiquid indivisible contingent claim in an incomplete semimartingale market environment. Under the assumption that the agents are exponential utility maximizers with non-traded random endowments, we provide necessary and sufficient conditions for negotiation to be successful, i.e.,… (More)