Yuri Kabanov

Bond Market Structure in the Presence of Marked Point Processes

We investigate the term structure of zero coupon bonds when interest rates are driven by a general marked point process as well as by a Wiener process. Developing a theory that allows for measure-valued trading portfolios, we study existence and uniqueness of a martingale measure. We also study completeness and its relation to the uniqueness of a martingale measure. For the case of a finite jump spectrum we give a fairly general completeness result and for a Wiener-Poisson model we prove the existence of a time-independent set of basic bonds. We also give sufficient conditions for the existence of an affine term structure. Copyright Blackwell Publishers Inc. 1997.

Hedging and Liquidation under Transaction Costs in Currency Markets

Abstract. We consider a general semimartingale model of a currency market with transaction costs and give a description of the initial endowments which allow to hedge a contingent claim in various currencies by a self-financing portfolio. As an application we obtain a result on the structure of optimal strategies for the problem of maximizing expected utility from terminal wealth.

Towards a General Theory of Bond Markets

Abstract.The main purpose of the paper is to provide a mathematical background for the theory of bond markets similar to that available for stock markets. We suggest two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions. Such integrals are used to define the evolution of the value of a portfolio of bonds corresponding to a trading strategy which is a measure-valued predictable process. The existence of an equivalent martingale measure is discussed and HJM-type conditions are derived for a jump-diffusion model. The question of market completeness is considered as a problem of the range of a certain integral operator. We introduce a concept of approximate market completeness and show that a market is approximately complete iff an equivalent martingale measure is unique.

Optional Decomposition and Lagrange Multipliers

Abstract. Let

A teacher’s note on no-arbitrage criteria

{\cal Q}

In the insurance business risky investments are dangerous

be the set of equivalent martingale measures for a given process

No-arbitrage criteria for financial markets with efficient friction

S

On Leland's strategy of option pricing with transactions costs

, and let

Asymptotic arbitrage in large financial markets

X

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

be a process which is a local supermartingale with respect to any measure in