数理金融

A simple statement and accessible proof of a version of the Fundamental Theorem of Asset Pricing in discrete time is provided. Careful distinction is made between prices and cash flows in order to provide uniform treatment of all…

We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem,…

The present article provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models as well as American barrier-type options under the Black & Scholes framework. Our method generalizes…

We provide a general probabilistic framework within which we establish scaling limits for a class of continuous-time stochastic volatility models with self-exciting jump dynamics. In the scaling limit, the joint dynamics of asset returns…

Stochastic bridges are commonly used to impute missing data with a lower sampling rate to generate data with a higher sampling rate, while preserving key properties of the dynamics involved in an unbiased way. While the generation of…

We prove that the variance swap rate (fair strike) equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary…

Indices of acceptability are well suited to frame the axiomatic features of many performance measures, associated to terminal random cash flows.We extend this notion to classes of c\`adl\`ag processes modelling cash flows over a fixed…

In this paper, we address one of the main puzzles in finance observed in the stock market by proponents of behavioral finance: the stock predictability puzzle. We offer a statistical model within the context of rational finance which can be…

We propose a model for the joint evolution of European inflation, the European Central Bank official interest rate and the short-term interest rate, in a stochastic, continuous time setting. We derive the valuation equation for a contingent…

Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried…

We develop a dual-control method for approximating investment strategies in incomplete environments that emerge from the presence of trading constraints. Convex duality enables the approximate technology to generate lower and upper bounds…

When dealing with Heston's stochastic volatility model, the change of measure from the subjective measure P to the objective measure Q is usually investigated under the assumption that the Feller condition is satisfied. This paper closes…

We establish dual representations for systemic risk measures based on acceptance sets in a general setting. We deal with systemic risk measures of both "first allocate, then aggregate" and "first aggregate, then allocate" type. In both…

The effects of weather on agriculture in recent years have become a major global concern. Hence, the need for an effective weather risk management tool (i.e., weather derivatives) that can hedge crop yields against weather uncertainties.…

This paper investigates a hybrid stochastic differential reinsurance and investment game between one reinsurer and two insurers, including a stochastic Stackelberg differential subgame and a non-zero-sum stochastic differential subgame. The…

It has often been stated that, within the class of continuous stochastic volatility models calibrated to vanillas, the price of a VIX future is maximized by the Dupire local volatility model. In this article we prove that this statement is…

This paper investigates calculations of robust funding valuation adjustment (FVA) for over the counter (OTC) derivatives under distributional uncertainty using Wasserstein distance as the ambiguity measure. Wrong way funding risk can be…

The present paper is devoted to the study of a bank salvage model with finite time horizon and subjected to stochastic impulse controls. In our model, the bank's default time is a completely inaccessible random quantity generating its own…

In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. This characterisation shows that it is indeed a well-chosen condition…

We derive a closed form solution for an optimal control problem related to an interbank lending schemes subject to terminal probability constraints on the failure of banks which are interconnected through a financial network. The derived…