International Journal of Theoretical and Applied Finance

A quadratic discrete time probabilistic model, for optimal portfolio selection, under risk constraint, is introduced in the context of (re-) insurance and finance. The portfolio is composed of contracts with arbitrary underwriting and maturity times. For positive values of underwriting levels, the expected value of the accumulated final result is optimized under constraints on its variance and on annual Returns On Equity. Existence of a unique solution is proved and a Lagrangian formalism is given. An effective method for solving the Euler-Lagrange equations is developed. The approximate determination of the multipliers is discussed. This basic model, which can include both assets and liabilities, is an important building block for more general models, with constraints also on non-solvency probabilities, market-shares, short-fall distributions and Values at Risk.

We provide a new way of hedging a commodity exposure which eliminates downside risk without sacrificing upside potential. The tool used is a variant on the equity passport option and can be used with both futures and forwards contracts as the underlying hedge instrument. Results are given for popular commodity price models such as Gibson-Schwartz and Black with convenience yield. Two different scenarios are considered, one where the producer places his usual hedge and undertakes additional trading, and the other where the usual hedge is not held. In addition, a comparison result is derived showing that one scenario is always more expensive than the other. The cost of these methods are compared to buying a put option on the commodity.

Traders are compensated by bonuses, in addition to their basic salary. However, little is known about how to optimally reward a trader. In this article we build a framework for the study of this problem and explore a variety of possible compensation structures.

We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic-risk minimisation scheme with history-dependent hedging strategies, we obtain a general formula, valid for weakly correlated non-Gaussian processes. We show that for Gaussian price increments, the correlations are irrelevant, and the Black-Scholes formula holds with the volatility of the price increments calculated on the scale of the re-hedging. For non-Gaussian processes, further non trivial corrections to the "smile" are brought about by the correlations, even when the hedge is the Black-Scholes Δ-hedge. We introduce a compact notation which eases the computations and could be of use to deal with more complicated models.

This paper aims to establish a set of necessary and sufficient conditions that the expression of a default free bond must verify in a situation in which spot rates of interest increase. In this case, if the agent divides the period of his investment, that is, if he disinvests and, immediately, re-invests his capital in different issues of bonds, can obtain an advantage in the final amount. In order to do this, necessary conditions include an approximation of the forward interest rate, that is to say the logarithmic density, its limits to +∞ and -∞ and the second generalized derivative of the bond price. Sufficient conditions involve an auxiliary function using these limits and, finally, necessary and sufficient conditions are related with the logarithm of the bond price.