相关论文: Well-Posedness and Comparison Principle for Option…

The coupled system, where one is a degenerate parabolic equation and the other has not a diffusion term arises in the modeling of European options with liquidity shocks. Two implicit-explicit (IMEX) schemes that preserve the positivity of…

We study the valuation and hedging problem of European options in a market subject to liquidity shocks. Working within a Markovian regime-switching setting, we model illiquidity as the inability to trade. To isolate the impact of such…

Paper is based on "The cost of illiquidity and its effects on hedging", L. C. G. Rogers and Surbjeet Singh, 2010. We generalize its thesis to constant elasticity model, which own previously used Black-Schoels model as a special case. The…

We propose a new model for electricity pricing based on the price cap principle. The particularity of the model is that the asset price is an exponential functional of a jump L\'evy process. This model can capture both mean reversion and…

This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a…

We consider a two-asset non-linear model of option pricing in an environment where the correlation is not known precisely, but varies between two known values. First we discuss the non-negativity of the solution of the equation. Next, we…

We study the pricing and hedging of European spread options on correlated assets when, in contrast to the standard framework and consistent with imperfect liquidity markets, the trading in the stock market has a direct impact on stocks…

In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage…

We study the problem of optimal pricing and hedging of a European option written on an illiquid asset $Z$ using a set of proxies: a liquid asset $S$, and $N$ liquid European options $P_i$, each written on a liquid asset $Y_i, i=1,N$. We…

This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and…

It is well known that, under standard assumptions, initial value problems for fractional ordinary differential equations involving Caputo-type derivatives are well posed in the sense that a unique solution exists and that this solution…

These lecture notes accompany two classes given at the NRHEP2 school. In the first lecture I introduce the basic concepts used for analyzing well-posedness, that is the existence of a unique solution depending continuously on given data, of…

Reliability Options are capacity remuneration mechanisms aimed at enhancing security of supply in electricity systems. They can be framed as call options on electricity sold by power producers to System Operators. This paper provides a…

We analyse a PDE system modelling poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes in the medium. We investigate the…

European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…

We prove well-posedness for a transport-diffusion problem coupled with a wave equation for the potential. We assume that the initial data are small. A bilinear form in the spirit of Kato's proof for the Navier-Stokes equations is used,…

In this paper, we propose an iterative splitting method to solve the partial differential equations in option pricing problems. We focus on the Heston stochastic volatility model and the derived two-dimensional partial differential equation…

We investigate the relation between the fair price for European-style vanilla options and the distribution of short-term returns on the underlying asset ignoring transaction and other costs. We compute the risk-neutral probability density…

We study linear integro-differential equations in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations are covered by the class of…

Here we develop an option pricing method based on Legendre series expansion of the density function. The key insight, relying on the close relation of the characteristic function with the series coefficients, allows to recover the density…