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We consider the pricing of American put options in a model-independent setting: that is, we do not assume that asset prices behave according to a given model, but aim to draw conclusions that hold in any model. We incorporate market…
Sustaining efficiency and stability by properly controlling the equity to asset ratio is one of the most important and difficult challenges in bank management. Due to unexpected and abrupt decline of asset values, a bank must closely…
We consider the problem of finding model-independent bounds on the price of an Asian option, when the call prices at the maturity date of the option are known. Our methods differ from most approaches to model-independent pricing in that we…
American options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties --volatility and…
We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson…
We study the optimal timing of derivative purchases in incomplete markets. In our model, an investor attempts to maximize the spread between her model price and the offered market price through optimally timing her purchase. Both the…
The continuous time model of dynamic asset trading is the central model of modern finance. Because trading cannot in fact take place at every moment of time, it would seem desirable to show that the continuous time model can be viewed as…
An investor with constant relative risk aversion and an infinite planning horizon trades a risky and a safe asset with constant investment opportunities, in the presence of small transaction costs and a binding exogenous portfolio…
Federal student loans are fixed-rate debt contracts with three main special features: (i) borrowers can use income-driven schemes to make payments proportional to their income above subsistence, (ii) after several years of good standing,…
Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for…
We consider an insurance company modelling its surplus process by a Brownian motion with drift. Our target is to maximise the expected exponential utility of discounted dividend payments, given that the dividend rates are bounded by some…
Cryptocurrency lending pools are services that allow lenders to pool together assets in one cryptocurrency and loan it out to borrowers who provide collateral worth more (than the loan) in a separate cryptocurrency. Borrowers can repay…
The aim of this paper is to solve an optimal investment, consumption and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic…
Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of…
We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an…
In financial markets, liquidity is not constant over time but exhibits strong seasonal patterns. In this article we consider a limit order book model that allows for time-dependent, deterministic depth and resilience of the book and…
It is known that the decision to purchase an annuity may be associated to an optimal stopping problem. However, little is known about optimal strategies, if the mortality force is a generic function of time and if the `subjective' life…
We study Markowitz's mean-variance portfolio selection problem in a continuous-time Black-Scholes market with different borrowing and saving rates. The associated Hamilton-Jacobi-Bellman equation is fully nonlinear. Using a delicate partial…
We consider a continuous-time financial market with no arbitrage and no transactions costs. In this setting, we introduce two types of perpetual contracts, one in which the payoff to the long side is a fixed function of the underlyers and…
We consider Merton's problem with proportional transaction costs. It is well known that the optimal investment strategy is characterized by two trading boundaries, the buy boundary and the sell boundary, between which lies the no-trading…