Related papers: A Stochastic Delay Model for Pricing Debt and Equi…
In this paper we present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. We demonstrate that the comonotonic setting provides a lower bound and Jensen's inequality provides an…
Much research in systemic risk is focused on default contagion. While this demands an understanding of valuation, fewer articles specifically deal with the existence, the uniqueness, and the computation of equilibrium prices in structural…
We provide closed-form market equilibrium formula consolidating informational imperfections and investors beliefs. Based on Merton's model, we characterize the equilibrium expected excess returns vector with incomplete information. We then…
Backward Stochastic Differential Equations (BSDEs) have been widely employed in various areas of social and natural sciences, such as the pricing and hedging of financial derivatives, stochastic optimal control problems, optimal stopping…
We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter (related to different symmetries of the crystal lattice in the phase…
This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's…
Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlying TDDEs from observed data remains a challenging problem…
We consider the problem of delay estimation by the observations of the solutions of several SDEs. It is known that the MLE for these models are consistent and asymptotically normal, but the likelihood ratio functions are not differentiable…
The concept of the path-dependent partial differential equation (PPDE) was first introduced in the context of path-dependent derivatives in financial markets. Its semilinear form was later identified as a non-Markovian backward stochastic…
We propose a novel strategy for multivariate extreme value index estimation. In applications such as finance, volatility and risk present in the components of a multivariate time series are often driven by the same underlying factors, such…
We address the Merton problem of maximizing the expected utility of terminal wealth using techniques from variational analysis. Under a general continuous semimartingale market model with stochastic parameters, we obtain a characterization…
In this paper we introduce a simple continuous-time asset pricing framework, based on general multi-dimensional diffusion processes, that combines semi-analytic pricing with a nonlinear specification for the market price of risk. Our…
In this paper, we propose a novel methodology for pricing equity-indexed annuities featuring cliquet-style payoff structures and early surrender risk, using advanced financial modeling techniques. Specifically, the market is modeled by an…
An efficient linear solver plays an important role while solving partial differential equations (PDEs) and partial integro-differential equations (PIDEs) type mathematical models. In most cases, the efficiency depends on the stability and…
The online weighted matching problem is a fundamental problem in machine learning due to its numerous applications. Despite many efforts in this area, existing algorithms are either too slow or don't take $\mathrm{deadline}$ (the longest…
Existing mathematical models of delay discounting (e. g. exponential model, hyperbolic model, and those derived from nonextensive statistics) consider impulsivity as a single entity. However, the present article derives a novel mathematical…
Delay-Differential Equations (DDEs) are the most common representation for systems with delay. However, the DDE representation is limited. In network models with delay, the delayed channels are low-dimensional and accounting for this…
The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
In this paper, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic…