A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios

A Stochastic Calculus Model of Continuous Trading: Complete Markets

A pappr by the same authors in the 1981 volume of Stochastic Processes artd Their Applications presented a general model, based on martingales and stochastic integrals, for the economic problem of investing in a portfolio of securities. In particular, and using the terminology developed therein, that paper stated that every integrable contingent claim is attainable (i.e., the model is complete)...

Optimal Trading with Stochastic Liquidity and Volatility

We consider the problem of mean-variance optimal agency execution strategies, when the market liquidity and volatility vary randomly in time. Under specific assumptions for the stochastic processes satisfied by these parameters, we construct a Hamilton–Jacobi–Bellman equation for the optimal cost and strategy. We solve this equation numerically and illustrate optimal strategies for varying risk...

Stochastic Calculus of Heston’s Stochastic-Volatility Model

The Heston stochastic-volatility model is a square-root diffusion model for the stochasticvariance. It gives rise to a singular diffusion for the distribution as noted by Feller (1951). Hence, there is an order constraint on the relationship between the limit that the variance goes to zero and the limit that time-step goes to zero, so that any non-trivial transformation of the Heston model lead...

Robustness of optimal portfolios under risk and stochastic dominance constraints

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Continuous-Time Model of Insider Trading