Related papers: Completeness of bond market driven by L\'evy proce…
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…
The property of perfectness plays an important role in the theory of Bayesian networks. First, the existence of perfect distributions for arbitrary sets of variables and directed acyclic graphs implies that various methods for reading…
In this paper we examine the claims reserving problem using Tweedie's compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated…
The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and…
We propose a model for the credit markets in which the random default times of bonds are assumed to be given as functions of one or more independent "market factors". Market participants are assumed to have partial information about each of…
This paper extends an option-theoretic approach to estimate liquidity spreads for corporate bonds. Inspired by Longstaff's equity market framework and subsequent work by Koziol and Sauerbier on risk-free zero-coupon bonds, the model views…
The paper studies the Heath-Jarrow-Morton-Musiela equation of the bond market. The equation is analyzed in weighted spaces of functions defined on $[0,+\infty)$. Sufficient conditions for local and global existence are obtained . For…
How should financial institutions hedge their balance sheets against interest rate risk when managing long-term assets and liabilities? We address this question by proposing a bond portfolio solution based on ambiguity-averse preferences,…
Hedging strategies in bond markets are computed by martingale representation and the Clark-Ocone formula under the choice of a suitable of numeraire, in a model driven by the dynamics of bond prices. Applications are given to the hedging of…
We model the term structure of the forward default intensity and the default density by using L\'evy random fields, which allow us to consider the credit derivatives with an after-default recovery payment. As applications, we study the…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving…
In the past decades, advanced probabilistic methods have had significant impact on the field of finance, both in academia and in the financial industry. Conversely, financial questions have stimulated new research directions in probability.…
In this paper, we present the testing of four hypotheses on two streams of observations that are driven by L\'evy processes. This is applicable for sequential decision making on the state of two-sensor systems. In one case, each sensor…
Upper estimates of densities of convolution semigroups of probability measures are given under explicit assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent.
We propose some machine-learning-based algorithms to solve hedging problems in incomplete markets. Sources of incompleteness cover illiquidity, untradable risk factors, discrete hedging dates and transaction costs. The proposed algorithms…
Many financial and economic variables, including financial returns, exhibit nonlinear dependence, heterogeneity and heavy-tailedness. These properties may make problematic the analysis of (non-)efficiency and volatility clustering in…
The purpose of this article is to introduce a new L\'evy process, termed Variance Gamma++ process, to model the dynamic of assets in illiquid markets. Such a process has the mathematical tractability of the Variance Gamma process and is…
We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the…
We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor…