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We consider the optimal investment problem when the traded asset may default, causing a jump in its price. For an investor with constant absolute risk aversion, we compute indifference prices for defaultable bonds, as well as a price for…
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…
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 work we study the continuous time exponential utility maximization problem in the framework of an investor who is informed about the price changes with a delay. This leads to a non-Markovian stochastic control problem. In the case…
This paper studies the optimal investment problem with random endowment in an inventory-based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules…
One approach to the analysis of stochastic fluctuations in market prices is to model characteristics of investor behaviour and the complex interactions between market participants, with the aim of extracting consequences in the aggregate.…
We consider an agent who has access to a financial market, including derivative contracts, who looks to maximise her utility. Whilst the agent looks to maximise utility over one probability measure, or class of probability measures, she…
Exponential functionals of Brownian motion have been extensively studied in financial and insurance mathematics due to their broad applications, for example, in the pricing of Asian options. The Black-Scholes model is appealing because of…
The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control…
Recently, Frazier et al. proposed a natural model for crowdsourced exploration of different a priori unknown options: a principal is interested in the long-term welfare of a population of agents who arrive one by one in a multi-armed bandit…
Stability of the utility maximization problem with random endowment and indifference prices is studied for a sequence of financial markets in an incomplete Brownian setting. Our novelty lies in the nonequivalence of markets, in which the…
We consider a mean-variance portfolio selection problem in a financial market with contagion risk. The risky assets follow a jump-diffusion model, in which jumps are driven by a multivariate Hawkes process with mutual-excitation effect. The…
The classical Markowitz mean-variance model uses variance as a risk measure and calculates frontier portfolios in closed form by using standard optimization techniques. For general mean-risk models such closed form optimal portfolios are…
We address the problem of sharing risk among agents with preferences modelled by a general class of comonotonic additive and law-based functionals that need not be either monotone or convex. Such functionals are called distortion…
This paper first describes a class of uncertain stochastic control systems with Markovian switching, and derives an It\^o-Liu formula for Markov-modulated processes. And we characterize an optimal control law, which satisfies the…
We consider a market impact game for $n$ risk-averse agents that are competing in a market model with linear transient price impact and additional transaction costs. For both finite and infinite time horizons, the agents aim to minimize a…
We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a…
Stochastic optimal control of dynamical systems is a crucial challenge in sequential decision-making. Recently, control-as-inference approaches have had considerable success, providing a viable risk-sensitive framework to address the…
This paper studies the optimal risk-averse timing to sell a risky asset. The investor's risk preference is described by the exponential, power, or log utility. Two stochastic models are considered for the asset price -- the geometric…