Related papers: Superhedging and Dynamic Risk Measures under Volat…
Stochastic symmetries and related invariance properties of finite dimensional SDEs driven by general c\`adl\`ag semimartingales taking values in Lie groups are defined and investigated. In order to enlarge the class of possible symmetries…
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the…
In this paper, we propose a suboptimal moving horizon estimator for a general class of nonlinear systems. For the stability analysis, we transfer the "feasibility-implies-stability/robustness" paradigm from model predictive control to the…
We find various exact solutions for a new stochastic volatility (SV) model: the transition probability density, European-style option values, and (when it exists) the martingale defect. This may represent the first example of an SV model…
We consider a multi-asset incomplete model of the financial market, where each of $m\geq 2$ risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide…
Using cumulative residual processes, we propose joint goodness-of-fit tests for conditional means and variances functions in the context of nonlinear time series with martingale difference innovations. The main challenge comes from the fact…
We propose a variational method to solve all three estimation problems for nonlinear stochastic dynamical systems: prediction, filtering, and smoothing. Our new approach is based upon a proper choice of cost function, termed the {\it…
We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
This paper features expectiles in dynamic and stochastic optimization. Expectiles are a family of risk functionals characterized as minimizers of optimization problems. For this reason, they enjoy various unique stability properties, which…
We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a two stage process that first determines admissible model…
Sublinear expectations for uncertain processes have received a lot of attention recently, particularly methods to extend a downward-continuous sublinear expectation on the bounded finitary functions to one on the non-finitary functions. In…
The density hypothesis on random times becomes now a standard in modeling of risks. One of the basic reasons to introduce the density hypothesis is the desire to have a computable credit risk model. However, recent work shows that merely an…
Systemic financial risk refers to the simultaneous failure or destabilization of multiple financial institutions, often triggered by contagion mechanisms or common exposures to shocks. In this paper, we present a dynamical model of bank…
In this paper, we consider a class of stochastic optimal control problems with risk constraints that are expressed as bounded probabilities of failure for particular initial states. We present here a martingale approach that diffuses a risk…
In this paper, we consider a risk-averse decision problem for controlled-diffusion processes, with dynamic risk measures, in which multiple risk-averse agents choose their decisions in such a way to minimize their individual accumulated…
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…
The objective of this paper is to establish the decomposition theorem for supermartingales under the $G$-framework. We first introduce a $g$-nonlinear expectation via a kind of $G$-BSDE and the associated supermartingales. We have shown…
We introduce the concept of stochastic measure-valued solutions to the complete Euler system describing the motion of a compressible inviscid fluid subject to stochastic forcing, where the nonlinear terms are described by defect measures.…
Systemic risk measures have been shown to be predictive of financial crises and declines in real activity. Thus, forecasting them is of major importance in finance and economics. In this paper, we propose a new forecasting method for…