Related papers: Bond Market Completeness and Attainable Contingent…
We introduce a discrete binary tree for pricing contingent claims with the underlying security prices exhibiting history dependence characteristic of that induced by market microstructure phenomena. Example dependencies considered include…
The framework of this article is cell motility modeling. Approximating cells as rigid spheres we take into account for both non-penetration and adhesions forces. Adhesions are modeled as a memory-like microscopic elastic forces. This leads…
Prices of tradables can only be expressed relative to each other at any instant of time. This fundamental fact should therefore also hold for contigent claims, i.e. tradable instruments, whose prices depend on the prices of other tradables.…
We introduce Hermite fractional financial markets, where market uncertainties are described by multidimensional Hermite motions. Hermite markets include as particular cases financial markets driven by multivariate fractional Brownian motion…
We prove the global existence of an incomplete, continuous-time finite-agent Radner equilibrium in which exponential agents optimize their expected utility over both running consumption and terminal wealth. The market consists of a traded…
Model uncertainty is a type of inevitable financial risk. Mistakes on the choice of pricing model may cause great financial losses. In this paper we investigate financial markets with mean-volatility uncertainty. Models for stock markets…
In this paper, we study the pricing of contracts in fixed income markets under volatility uncertainty in the sense of Knightian uncertainty or model uncertainty. The starting point is an arbitrage-free bond market under volatility…
We consider randomized computation of continuous data in the sense of Computable Analysis. Our first contribution formally confirms that it is no loss of generality to take as sample space the Cantor space of infinite FAIR coin flips. This…
The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent…
We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of…
We consider a one-period market model composed by a risk-free asset and a risky asset with $n$ possible future values (namely, a $n$-nomial market model). We characterize the lower envelope of the class of equivalent martingale measures in…
We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…
We consider the nonabelian sandpile model defined on directed trees by Ayyer, Schilling, Steinberg and Thi\'ery (Commun. Math. Phys, 2013) and restrict it to the special case of a one-dimensional lattice of $n$ sites which has open…
Mathematical models for financial asset prices which include, for example, stochastic volatility or jumps are incomplete in that derivative securities are generally not replicable by trading in the underlying. In earlier work (2004) the…
We introduce the entropic measure transform (EMT) problem for a general process and prove the existence of a unique optimal measure characterizing the solution. The density process of the optimal measure is characterized using a…
We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets. Both the asset value and the volatility processes are correlated through systemic Brownian motions, with default determined by…
We introduce a bond portfolio management theory based on foundations similar to those of stock portfolio management. A general continuous-time zero-coupon market is considered. The problem of optimal portfolios of zero-coupon bonds is…
In this paper we study dynamic backward problems, with the computation of conditional expectations as a main objective, in a framework where the (forward) state process satisfies a Volterra type SDE, with fractional Brownian motion as a…
Global existence for the nonisentropic compressible Euler equations with vacuum boundary for all adiabatic constants $\gamma > 1$ is shown through perturbations around a rich class of background nonisentropic affine motions. The notable…
We present a unified, market-complete model that integrates both the Bachelier and Black-Scholes-Merton frameworks for asset pricing. The model allows for the study, within a unified framework, of asset pricing in a natural world that…