Related papers: A Dynamic Correlation Modelling Framework with Con…
We propose two structural models for stochastic losses given default which allow to model the credit losses of a portfolio of defaultable financial instruments. The credit losses are integrated into a structural model of default events…
We present a nonlinear model predictive control (MPC) scheme for tracking of dynamic target signals. The scheme combines stabilization and dynamic trajectory planning in one layer, thus ensuring constraint satisfaction irrespective of…
We present an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities in a discrete time setup using theory of dynamic acceptability indices. In the first part of the paper we develop the theory of…
This thesis develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time finance, does not rely on stochastic integrals or other probabilistic…
This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other…
A simple graphical model for correlated defaults is proposed, with explicit formulas for the loss distribution. Algebraic geometry techniques are employed to show that this model is well posed for default dependence: it represents any given…
We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, including default of the investor. We illustrate the symmetry in the valuation and show that the adjustment…
In this paper we propose a copula contagion mixture model for correlated default times. The model includes the well known factor, copula, and contagion models as its special cases. The key advantage of such a model is that we can study the…
This paper introduces a unified micro-level stochastic framework for the joint modeling of loss reserves (RBNS), incurred but not reported (IBNR) reserves, and unearned premium risk under dependence, inflation, and discounting. The proposed…
We follow a long path for Credit Derivatives and Collateralized Debt Obligations (CDOs) in particular, from the introduction of the Gaussian copula model and the related implied correlations to the introduction of arbitrage-free dynamic…
Derivatives, as a critical class of financial instruments, isolate and trade the price attributes of risk assets such as stocks, commodities, and indices, aiding risk management and enhancing market efficiency. However, traditional hedging…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
The pricing of derivatives tied to baskets of assets demands a sophisticated framework that aligns with the available market information to capture the intricate non-linear dependency structure among the assets. We describe the dynamics of…
Car-following behavior modeling is critical for understanding traffic flow dynamics and developing high-fidelity microscopic simulation models. Most existing impulse-response car-following models prioritize computational efficiency and…
Purpose: This study introduces a novel framework for identifying and exploiting predictive lead-lag relationships in financial markets. We propose an integrated approach that combines advanced statistical methodologies with machine learning…
Consistent Recalibration models (CRC) have been introduced to capture in necessary generality the dynamic features of term structures of derivatives' prices. Several approaches have been suggested to tackle this problem, but all of them,…
The modeling of the probability of joint default or total number of defaults among the firms is one of the crucial problems to mitigate the credit risk since the default correlations significantly affect the portfolio loss distribution and…
We study dropout regularization in continuous-time models through the lens of random-batch methods -- a family of stochastic sampling schemes originally devised to reduce the computational cost of interacting particle systems. We construct…