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We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…
This paper considers nonlinear regular-singular stochastic optimal control of large insurance company. The company controls the reinsurance rate and dividend payout process to maximize the expected present value of the dividend pay-outs…
The classical optimal trading problem is the closure of a position in an asset over a time interval; the trader maximizes an expected utility under the constraint that the position be fully closed by terminal time. Since the asset price is…
We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. We show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio…
We consider the problem of minimizing capital at risk in the Black-Scholes setting. The portfolio problem is studied given the possibility that a correlation constraint between the portfolio and a financial index is imposed. The optimal…
This paper studies the properties of the optimal portfolio-consumption strategies in a {finite horizon} robust utility maximization framework with different borrowing and lending rates. In particular, we allow for constraints on both…
This work studies equilibrium problems under uncertainty where firms maximize their profits in a robust way when selling their output. Robust optimization plays an increasingly important role when best guaranteed objective values are to be…
In this short note, we study an optimization problem of expected implementation shortfall (IS) cost under general shaped market impact functions. In particular, we find that an optimal strategy is a VWAP (volume weighted average price)…
In this paper we consider the problem of minimising drawdown in a portfolio of financial assets. Here drawdown represents the relative opportunity cost of the single best missed trading opportunity over a specified time period. We formulate…
We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…
The dynamic portfolio optimization problem in finance frequently requires learning policies that adhere to various constraints, driven by investor preferences and risk. We motivate this problem of finding an allocation policy within a…
We study optimal investment in a financial market having a finite number of assets from a signal processing perspective. We investigate how an investor should distribute capital over these assets and when he should reallocate the…
To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by the characteristics of the order flow and…
A discrete time probabilistic model, for optimal equity allocation and portfolio selection, is formulated so as to apply to (at least) reinsurance. In the context of a company with several portfolios (or subsidiaries), representing both…
Once there is a decision of rebalancing or updating a portfolio of funds, the process of changing the current portfolio to the target one, involves a set of transactions that are susceptible of being optimized. This is particularly relevant…
We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following a diffusion with stochastic volatility. In the current financial market especially, it is important to…
We propose a data-driven portfolio selection model that integrates side information, conditional estimation and robustness using the framework of distributionally robust optimization. Conditioning on the observed side information, the…
This paper deals with numerical solutions to an impulse control problem arising from optimal portfolio liquidation with bid-ask spread and market price impact penalizing speedy execution trades. The corresponding dynamic programming (DP)…
We consider the problem of optimal investment with random endowment in a Black--Scholes market for an agent with constant relative risk aversion. Using duality arguments, we derive an explicit expression for the optimal trading strategy,…
In these notes we discuss investment allocation to multiple alpha streams traded on the same execution platform, including when trades are crossed internally resulting in turnover reduction. We discuss approaches to alpha weight…