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In this paper we study the pricing and hedging problem of a portfolio of life insurance products under the benchmark approach, where the reference market is modelled as driven by a state variable following a polynomial diffusion on a…
We investigate model risk and distributionally robust optimization (DRO) under marginal and martingale constraints. Building on our previous work, we address the previously open case of static hedging with second-period maturity vanilla…
There is empirical evidence that recovery rates tend to go down just when the number of defaults goes up in economic downturns. This has to be taken into account in estimation of the capital against credit risk required by Basel II to cover…
Portfolio optimization approaches inevitably rely on multivariate modeling of markets and the economy. In this paper, we address three sources of error related to the modeling of these complex systems: 1. oversimplifying hypothesis; 2.…
Explicitly taking into account the risk incurred when borrowing at a shorter tenor versus lending at a longer tenor ("roll-over risk"), we construct a stochastic model framework for the term structure of interest rates in which a frequency…
The percolation, Ising, and O($n$) models constitute fundamental systems in statistical and condensed matter physics. For short-range-interacting cases, the nature of their phase transitions is well established by renormalization-group…
In our model, private actors with interbank cash flows similar to, but nore general than (Carmona, Fouque, Sun, 2013) borrow from the outside economy at a certain interest rate, controlled by the central bank, and invest in risky assets.…
The local distributions of the one-dimensional dilute annealed Ising model with charged impurities are studied. Explicit expressions are obtained for the pair distribution functions and correlation lengths, and their low-temperature…
The paper studies derivative asset analysis in structural credit risk models where the asset value of the firm is not fully observable. It is shown that in order to compute the price dynamics of traded securities one needs to solve a…
This article investigates the asymptotic distribution of penalized estimators with non-differentiable penalties designed to recover low-dimensional pattern structures. Patterns play a central role in estimation, as they reveal the…
We present a robust Deep Hedging framework for the pricing and hedging of option portfolios that significantly improves training efficiency and model robustness. In particular, we propose a neural model for training model embeddings which…
We develop a finite horizon continuous time market model, where risk averse investors maximize utility from terminal wealth by dynamically investing in a risk-free money market account, a stock written on a default-free dividend process,…
A transfer matrix scaling technique is developed for randomly diluted systems, and applied to the site-diluted Ising model on a square lattice in two dimensions. For each allowed disorder configuration between two adjacent columns, the…
We study pricing and hedging under parameter uncertainty for a class of Markov processes which we call generalized affine processes and which includes the Black-Scholes model as well as the constant elasticity of variance (CEV) model as…
We study the out-of-equilibrium probability distribution function of the local order parameter in the transverse field Ising quantum chain. Starting from a fully polarised state, the relaxation of the ferromagnetic order is analysed: we…
We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network, subject to an exogenous macroeconomic shock. We show that, under some regularity assumptions, the default cascade model…
A theory of symbolic dynamic systems with long-range correlations based on the consideration of the binary N-step Markov chains developed earlier in Phys. Rev. Lett. 90, 110601 (2003) is generalized to the biased case (non equal numbers of…
We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of four-fold coordinated sites connected via variable length one-dimensional chains.…
In this paper, we have studied the pricing of a continuously collateralized CDS. We have made use of the "survival measure" to derive the pricing formula in a straightforward way. As a result, we have found that there exists irremovable…
We develop a novel multivariate semi-parametric framework for joint portfolio Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting. Unlike existing univariate semi-parametric approaches, the proposed framework explicitly models the…