数理金融
The virtue of an American option is that it can be exercised at any time. This right is particularly valuable when there is model uncertainty. Yet almost all the extensive literature on American options assumes away model uncertainty. This…
Employing the Klein-Gordon equation, we propose a generalized Black-Scholes equation. In addition, we found a limit where this generalized equation is invariant under conformal transformations, in particular invariant under scale…
Our goal here is to discuss the pricing problem of European and American options in discrete time using elementary calculus so as to be an easy reference for first year undergraduate students. Using the binomial model we compute the fair…
We study regularity properties of the dynamic value functions of primal and dual problems of optimal investing for utility functions defined on the whole real line. Relations between decomposition terms of value processes of primal and dual…
We propose a model for the credit and liquidity risks faced by clearing members of Central Counterparty Clearing houses (CCPs). This model aims to capture the features of: gap risk; feedback between clearing member default, market…
We provide conditions for the existence and the unicity of strictly stationary solutions of the usual Dynamic Conditional Correlation GARCH models (DCC-GARCH). The proof is based on Tweedie's (1988) criteria, after having rewritten…
In this paper, we consider the problem of pricing discretely-sampled variance swaps based on a hybrid model of stochastic volatility and stochastic interest rate with regime-switching. Our modelling framework extends the Heston stochastic…
Functional portfolio generation, initiated by E.R. Fernholz almost twenty years ago, is a methodology for constructing trading strategies with controlled behavior. It is based on very weak and descriptive assumptions on the covariation…
In this article, we investigate the behavior of long-term options. In many cases, option prices follow an exponential decay (or growth) rate for further maturity dates. We determine under what conditions option prices are characterized by…
We consider an insurance entity endowed with an initial capital and a surplus process modelled as a Brownian motion with drift. It is assumed that the company seeks to maximise the cumulated value of expected discounted dividends, which are…
We study a robust portfolio optimization problem under model uncertainty for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible L\'evy triplets; that is, possible instantaneous drift, volatility…
We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities.…
We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The…
This paper studies a class of optimal multiple stopping problems driven by L\'evy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real…
This paper studies convex duality in optimal investment and contingent claim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions…
We introduce and study a class of over-the-counter market models specified by systems of Ordinary Differential Equations (ODE's), in the spirit of Duffie- G^arleanu-Pedersen [6]. The key innovation is allowing for multiple assets. We show…
In this paper we study the pricing and hedging of structured products in energy markets, such as swing and virtual gas storage, using the exponential utility indifference pricing approach in a general incomplete multivariate market model…
We introduce a formal language IE that is a variant of the language PAL developed in [van Benthem 2011] by adding a belief operator and a common belief operator,specializing to stochastic analysis. A constant symbol in the language denotes…
We study the concept of financial bubble in a market model endowed with a set of probability measures, typically mutually singular to each other. In this setting we introduce the notions of robust bubble and robust fundamental value in a…
This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other…