A Note on the Two-fund Separation Theorem

This note contains two remarks on the traditional capital asset pricing model (CAPM) with one risk-free asset. Firstly, an elementary proof of the two-fund separation theorem is provided showing that asset-demand may become undefined if the limiting slope of the investor's indifference curves is finite. Secondly, it is shown that an additional limiting condition on the risk aversion is generally necessary to guarantee existence of an equilibrium in the CAPM with one risk-free asset. The role of these two limiting conditions seems to have been overlooked in the established literature. A generalized existence result is formulated which allows for the case in which in equilibrium not all investors participate in the market for risky assets.Portfolio choice, CAPM, risk aversion, equilibrium, market participation

DARA and DRRA option bounds from concurrently expiring options

In this paper we derive option bounds from concurrently expiring options assuming the representative investor has decreasing absolute {relative} risk aversion. We show that given the prices of the underlying stock and n concurrently expiring options, the DARA {DRRA} option bound is given by a representative investor who has piecewise constant absolute {relative} risk aversion. We also derive option bounds from concurrently expiring option prices assuming the representative investor has decreasing and bounded absolute {relative} risk aversion

Forward Exponential Performances: Pricing and Optimal Risk Sharing

In a Markovian stochastic volatility model, we consider financial agents whose investment criteria are modelled by forward exponential performance processes. The problem of contingent claim indifference valuation is first addressed and a number of properties are proved and discussed. Special attention is given to the comparison between the forward exponential and the backward exponential utility indifference valuation. In addition, we construct the problem of optimal risk sharing in this forward setting and solve it when the agents' forward performance criteria are exponential.Comment: 29 page

Asymmetric information, self-selection and pricing of insurance contracts: the simple no-claims case

This paper presents an optional bonus-malus contract based on a pri-ori risk classification of the underlying insurance contract. By inducing self-selection, the purchase of the bonus-malus contract can be used as a screening device. This gives an even better pricing performance than both an experience rating scheme and a classical no-claims bonus system. An application to the Danish automobile insurance market is considered

Approximation solutions for indifference pricing under general utility functions

With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners use: Best Estimate plus a "Market Value Margin". Furthermore, we compare our approximations to known analytical results for exponential and power utility

Utility based pricing and hedging of jump diffusion processes with a view to applications

We discuss utility based pricing and hedging of jump diffusion processes with emphasis on the practical applicability of the framework. We point out two difficulties that seem to limit this applicability, namely drift dependence and essential risk aversion independence. We suggest to solve these by a re-interpretation of the framework. This leads to the notion of an implied drift. We also present a heuristic derivation of the marginal indifference price and the marginal optimal hedge that might be useful in numerical computations.Comment: 23 pages, v2: publishe

Continuous Equilibrium in Affine and Information-Based Capital Asset Pricing Models

We consider a class of generalized capital asset pricing models in continuous time with a finite number of agents and tradable securities. The securities may not be sufficient to span all sources of uncertainty. If the agents have exponential utility functions and the individual endowments are spanned by the securities, an equilibrium exists and the agents' optimal trading strategies are constant. Affine processes, and the theory of information-based asset pricing are used to model the endogenous asset price dynamics and the terminal payoff. The derived semi-explicit pricing formulae are applied to numerically analyze the impact of the agents' risk aversion on the implied volatility of simultaneously-traded European-style options.Comment: 24 pages, 4 figure