Utility based pricing of contingent claims

In a discrete setting, we develop a model for pricing a contingent claim. Since the presence of hedging opportunities influences the price of a contingent claim, first we introduce the optimal hedging strategy assuming a contingent claim has been issued: a strategy implemented by investing the budget plus the selling price is optimal if it maximizes the expected utility of the agent's revenue, which is the difference between the outcome of the hedging portfolio and the payoff of the claim. Next, we introduce the `reservation price' as a subjective valuation of a contingent claim. This is defined as the minimum price to be added to the initial budget that makes the issue of the claim more preferable than optimally investing in the available securities. We define the reservation price both for a short position (reservation selling price) and for a long position (reservation buying price) in the contingent claim. When the contingent claim is redundant, both the selling and the buying price collapse in the usual Arrow-Debreu price. We develop a numerical procedure to evaluate the reservation price and two applications are provided. Different utility functions are used and some qualitative properties of the reservation price are shown.Incomplete markets, reservation price, expected utility, optimization

Moduli Spaces of Curves with Homology Chains and c=1 Matrix Models

We show that introducing a periodic time coordinate in the models of Penner-Kontsevich type generalizes the corresponding constructions to the case of the moduli space ${\cal S}_{gn}^k$ of curves $C$ with homology chains \gamma\in H_1(C,\zet_k). We make a minimal extension of the resulting models by adding a kinetic term, and we get a new matrix model which realizes a simple dynamics of \zet_k-chains on surfaces. This gives a representation of $c=1$ matter coupled to two-dimensional quantum gravity with the target space being a circle of finite radius, as studied by Gross and Klebanov.Comment: IFUM 459/FT (LaTeX, 9 pages; a few misprints have been corrected and the introduction has been slightly modified

Mean Field Approach to the Giant Wormhole Problem

We introduce a gaussian probability density for the space-time distribution of wormholes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic ``large'' universe.Comment: 10 pages, Late

Non-linear WKB Analysis of the String Equation

We apply non-linear WKB analysis to the study of the string equation. Even though the solutions obtained with this method are not exact, they approximate extremely well the true solutions, as we explicitly show using numerical simulations. ``Physical'' solutions are seen to be separatrices corresponding to degenerate Riemann surfaces. We obtain an analytic approximation in excellent agreement with the numerical solution found by Parisi et al. for the $k=3$ case.Comment: 21 pages. To appear in the proceedings of the Research Conference on Advanced Quantum Field Theory and Critical Phenomena, held in Como (Italy), June 17-21, 1991 -- World Scientifi

Capital Regulation, Liquidity Requirements and Taxation in a Dynamic Model of Banking

This paper formulates a dynamic model of a bank exposed to both credit and liquidity risk, which can resolve financial distress in three costly forms: fire sales, bond issuance and equity issuance. We use the model to analyze the impact of capital regulation, liquidity requirements and taxation on banks' optimal policies and metrics of efficiency of intermediation and social value. We obtain three main results. First, mild capital requirements increase bank lending, bank efficiency and social value relative to an unregulated bank, but these benefits turn into costs if capital requirements are too stringent. Second, liquidity requirements reduce bank lending, efficiency and social value significantly, they nullify the benifits of mild capital requirements, and their private and social costs increase monotonically with their stringency. Third, increases in corporate income and bank liabilities taxes reduce bank lending, bank effciency and social value, with tax receipts increasing with the former but decreasing with the latter. Moreover, the effects of an increase in both forms of taxation are dampened if they are jointly implemented with increases in capital and liquidity requirements.Capital requirements;liquidity requirements;taxation of liabilities. JEL Classifications