Hansen and Jagannathan (1991) provide a lower bound on the variance of a stochastic discount factor (SDF). As many asset pricing models can be represented by using an SDF (see, e.g., Cochrane [2001] and references therein), this bound became instantly known as the Hansen-Jagannathan bound and has been applied widely in a variety of finance problems. On developing related bounds, Snow (1991) der...

In this paper, we point out that the widely used stochastic discount factor (SDF) methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear factor model. The first problem is that risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF...

In this paper, we propose a novel test of the 3M-CAPM under a positivity constraint on the estimated stochastic discount factor (SDF) and, more importantly, an upper bound on its volatility. The positivity constraint rules out arbitrage opportunities, while the restriction on SDF volatility rules out unduly large Sharpe ratios and is based on a sensible upper bound on investors’ risk aversion. ...

We demonstrate that for the sine-Gordon theory at the free fermion point, the 2point correlation functions of the fields exp(iαΦ) for 0 < α < 1 can be parameterized in terms of a solution to a sinh-Gordon-like equation. This result is derived by summing over intermediate multiparticle states and using the form factors to express this as a Fredholm determinant. The proof of the differential equa...

We revisit the issue of counting all local fields of the restricted sine-Gordon model, in the case corresponding to a perturbation of minimal unitary conformal field theory. The problem amounts to the study of a quotient of certain space of polynomials which enter the integral representation for form factors. This space may be viewed as a q-analog of the space of conformal coinvariants associat...

A cost-based approach to asset-pricing equilibrium relationships is developed. A cost function induces a stochastic discount factor (pricing kernel) that is a function of random output, prices, and capital stockt. By eliminating opportunities for arbitrage between financial markets and the production technology, firms minimize the current cost of future consumption. The first-order conditions f...

The aim of the paper is to analyze the impact of heterogeneous beliefs in an otherwise standard competitive complete market economy. The construction of a consensus probability belief, as well as a consensus consumer, are shown to be valid modulo an aggregation bias, which takes the form of a discount factor. In classical cases, the consensus probability belief is a risk tolerance weighted aver...