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Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. We propose a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in…
We study the problem of dynamically trading multiple futures whose underlying asset price follows a multiscale central tendency Ornstein-Uhlenbeck (MCTOU) model. Under this model, we derive the closed-form no-arbitrage prices for the…
We investigate the adaptive robust control framework for portfolio optimization and loss-based hedging under drift and volatility uncertainty. Adaptive robust problems offer many advantages but require handling a double optimization problem…
This paper studies the multi-period mean-variance portfolio allocation problem with transaction costs. Many methods have been proposed these last years to challenge the famous uni-period Markowitz strategy.But these methods cannot integrate…
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…
We discuss the improvement in the accuracy of a Monte Carlo integration that can be obtained by optimization of the `a-priori weights' of the various channels. These channels may be either the strata in a stratified-sampling approach, or…
We consider the problem of portfolio optimization with a correlation constraint. The framework is the multiperiod stochastic financial market setting with one tradable stock, stochastic income and a non-tradable index. The correlation…
We have designed an innovative portfolio rebalancing mechanism termed the Cascading Waterfall Round Robin Mechanism. This algorithmic approach recommends an ideal size and number of trades for each asset during the periodic rebalancing…
This paper investigates dynamic and static fund separations and their stability for long-term optimal investments under three model classes. An investor maximizes the expected utility with constant relative risk aversion under an incomplete…
For long term investments, model portfolios are defined at the level of indexes, a setup known as Strategic Asset Allocation (SAA). The possible outcomes at a scale of a few decades can be obtained by Monte Carlo simulations, resulting in a…
This paper investigates a time-inconsistent portfolio selection problem in the incomplete mar ket model, integrating expected utility maximization with risk control. The objective functional balances the expected utility and variance on log…
In this paper, we consider a frequency-based portfolio optimization problem with $m \geq 2$ assets when the expected logarithmic growth (ELG) rate of wealth is used as the performance metric. With the aid of the notion called dominant…
Collateral optimization refers to the systematic allocation of financial assets to satisfy obligations or secure transactions, while simultaneously minimizing costs and optimizing the usage of available resources. {This involves assessing…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
This paper studies the problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies. The market model considered is continuous in time and incomplete. the…
We consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing Jeffreys' non-informative prior and the conjugate informative prior, we derive stochastic representations for the…
Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization…
This paper studies some unconventional utility maximization problems when the ratio type relative portfolio performance is periodically evaluated over an infinite horizon. Meanwhile, the agent is prohibited from short-selling stocks. Our…
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…
Optimal multi-asset trading with Markovian predictors is well understood in the case of quadratic transaction costs, but remains intractable when these costs are $L_1$. We present a mean-field approach that reduces the multi-asset problem…