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Fractional Ornstein-Uhlenbeck processes

The classical stationary Ornstein-Uhlenbeck process can be obtained in two different ways. On the one hand, it is a stationary solution of the Langevin equation with Brownian motion noise. On the…
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Dynamic Monetary Risk Measures for Bounded Discrete-Time Processes

We study dynamic monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a dynamic risk…
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Arbitrage in fractional Brownian motion models

This work constructs arbitrage strategies for a financial market that consists of a money market account and a stock whose discounted price follows a fractional Brownian motion with drift or an exponential fractionalBrownianmotion with drift and shows how arbitrage can be excluded by restricting the class of trading strategies.
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Equivalent and absolutely continuous measure changes for jump-diffusion processes

We provide explicit sufficient conditions for absolute continuity and equivalence between the distributions of two jump-diffusion processes that can explode and be killed by a potential.
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Deep Optimal Stopping

A deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples is developed, broadly applicable in situations where the underlying randomness can efficiently be simulated.
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Market Price of Risk Specifications for Affine Models: Theory and Evidence

We extend the standard specification of the market price of risk for affine yield models of the term structure of interest rates, and estimate several models using the extended specification. For…
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RISK MEASURES ON ORLICZ HEARTS

Coherent, convex, and monetary risk measures were introduced in a setup where uncertain outcomes are modeled by bounded random variables. In this paper, we study such risk measures on Orlicz hearts.…
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COMPOSITION OF TIME-CONSISTENT DYNAMIC MONETARY RISK MEASURES IN DISCRETE TIME

In discrete time, every time-consistent dynamic monetary risk measure can be written as a composition of one-step risk measures. We exploit this structure to give new dual representation results for…
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Market price of risk speci-fications for a ne models: theory and evidence

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Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs

For a d‐dimensional diffusion of the form dXt = μ(Xt)dt + σ(Xt)dWt and continuous functions f and g, we study the existence and uniqueness of adapted processes Y, Z, Γ, and A solving the second‐order…
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