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We study scaled trinomial models converging to the Black--Scholes model, and analyze exponential certainty-equivalent prices for path-dependent European options. As the number of trading dates $n$ tends to infinity and the risk aversion is…
In this note, Black--Scholes implied volatility is expressed in terms of various optimisation problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries…
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models…
We formulate conditions for the solvability of the problem of robust utility maximization from final wealth in continuous time financial markets, without assuming weak compactness of the densities of the uncertainty set, as customary in the…
We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value…
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and…
We study expected utility maximization problem with constant relative risk aversion utility function in a complete market under the reinforcement learning framework. To induce exploration, we introduce the Tsallis entropy regularizer, which…
We consider an insurance company whose surplus is represented by the classical Cramer-Lundberg process. The company can invest its surplus in a risk free asset and in a risky asset, governed by the Black-Scholes equation. There is a…
This paper investigates well posedness of utility maximization problems for financial markets where stock returns depend on a hidden Gaussian mean reverting drift process. Since that process is potentially unbounded, well posedness cannot…
A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of…
The effectiveness of utility-maximization techniques for portfolio management relies on our ability to estimate correctly the parameters of the dynamics of the underlying financial assets. In the setting of complete or incomplete financial…
We study a utility maximization problem in a financial market with a stochastic drift process, combining a worst-case approach with filtering techniques. Drift processes are difficult to estimate from asset prices, and at the same time…
We consider a continuous-time market with proportional transaction costs. Under appropriate assumptions we prove the existence of optimal strategies for investors who maximize their worst-case utility over a class of possible models. We…
In this paper we derive the exact solution of the multi-period portfolio choice problem for an exponential utility function under return predictability. It is assumed that the asset returns depend on predictable variables and that the joint…
A continuous-time consumption-investment model with constraint is considered for a small investor whose decisions are the consumption rate and the allocation of wealth to a risk-free and a risky asset with logarithmic Brownian motion…
We maximize the expected utility of terminal wealth in an incomplete market where there are cone constraints on the investor's portfolio process and the utility function is not assumed to be strictly concave or differentiable. We establish…
Prompted by a recent experiment by Victor Haghani and Richard Dewey, this note generalises the Kelly strategy (optimal for simple investment games with log utility) to a large class of practical utility functions and including the effect of…
This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies' performances in the future market, which…
This paper studies a portfolio allocation problem, where the goal is to prescribe the wealth distribution at the final time. We study this problem with the tools of optimal mass transport. We provide a dual formulation which we solve by a…
We discuss an optimal investment, consumption and insurance problem of a wage earner under inflation. Assume a wage earner investing in a real money account and three asset prices, namely: a real zero coupon bond, the inflation-linked real…