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We consider the problem of governing systemic risk in an assets-liabilities dynamical model of banking system. In the model considered each bank is represented by its assets and its liabilities.The capital reserves of a bank are the…
In this paper, we explore an optimal timing strategy for the trading of price spreads exhibiting mean-reverting characteristics. A sequential optimal stopping framework is formulated to analyze the optimal timings for both entering and…
This paper studies the stochastic modeling of market drawdown events and the fair valuation of insurance contracts based on drawdowns. We model the asset drawdown process as the current relative distance from the historical maximum of the…
We perform a detailed theoretical study of the value of a class of participating policies with four key features: $(i)$ the policyholder is guaranteed a minimum interest rate on the policy reserve; $(ii)$ the contract can be terminated by…
We obtain option pricing formulas for stock price models in which the drift and volatility terms are functionals of a continuous history of the stock prices. That is, the stock dynamics follows a nonlinear stochastic functional differential…
In a classical optimal stopping problem in continuous time, the agent can choose any stopping time without constraint. Dupuis and Wang (Optimal stopping with random intervention times, Advances in Applied Probability, 34, 141--157, 2002)…
We study market-consistent valuation of liability cash flows motivated by current regulatory frameworks for the insurance industry. Building on the theory on multiple-prior optimal stopping we propose a valuation functional with sound…
In this work, I address the issue of forming riskless hedge in the continuous time option pricing model with stochastic stock volatility. I show that it is essential to verify whether the replicating portfolio is self-financing, in order…
We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities $\mathcal{P}$. The maturity is specified as the hitting time to level $0$ of…
In the context of dealing with financial risk management problems it is desirable to have accurate bounds for option prices in situations when pricing formulae do not exist in the closed form. A unified approach for obtaining upper and…
An agent holds a position in a perpetual contract with payoff function $\psi$ and attempts to liquidate the position while managing transaction costs, inventory risk, and funding rate payments. By solving the agent's stochastic control…
Managing unemployment is one of the key issues in social policies. Unemployment insurance schemes are designed to cushion the financial and morale blow of loss of job but also to encourage the unemployed to seek new jobs more pro-actively…
This paper studies the valuation of a class of default swaps with the embedded option to switch to a different premium and notional principal anytime prior to a credit event. These are early exercisable contracts that give the protection…
Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in…
This paper discusses the valuation of credit default swaps, where default is announced when the reference asset price has gone below certain level from the last record maximum, also known as the high-water mark or drawdown. We assume that…
We develop a theory which applies to any market dynamics that satisfy a fair market assumption on the nullity of the average profit of simple market making strategies. We show that for any such fair market, there exists a martingale fair…
In this paper we consider stopping problems for continuous-time Markov chains under a general risk-sensitive optimization criterion for problems with finite and infinite time horizon. More precisely our aim is to maximize the certainty…
We present a model of credit card profitability, assuming that the card-holder always pays the full outstanding balance. The motivation for the model is to calculate an optimal credit limit, which requires an expression for the expected…
Short sales are regarded as negative purchases in textbook asset pricing theory. In reality, however, the symmetry between purchases and short sales is broken by a variety of costs and risks peculiar to the latter. We formulate an optimal…
In credit risk literature, the existence of an equivalent martingale measure is stipulated as one of the main assumptions in the hazard process model. Here we show by construction the existence of a measure that turns the discounted stock…