We develop a non-negative polynomial minimum-norm likelihood ratio (PLR) of two distributions of which only moments are known. The PLR converges to the true, unknown, likelihood ratio. We show consistency, obtain the asymptotic distribution for the PLR coefficients estimated with sample moments,...

We consider portfolio selection under nonparametric alpha-maxmin ambiguity in the neighbourhood of a reference distribution. We show strict concavity of the portfolio problem under ambiguity aversion.Implied demand functions are nondifferentiable, resemble observed bid-ask spreads, and are...

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions...

This paper introduces a model-free decomposition of S&P 500 forward market index returns in terms of realized and implied dispersion, downside, and tail risk using option portfolios. The decomposition lends itself by construction to learn about the different sources of risk in the market return,...

Realized divergence gauges the distinct realized moments associated with time-varying uncertainty and is tradeable with divergence swaps engineered from delta-hedged option portfolios. Consistently with established notions of symmetry in arbitrage-free option markets, implied divergence...

We develop Residual MisPricing (RMP), an index capturing mispricing relative to a linear benchmark asset pricing model, from the structure imposed by no-arbitrage. RMP is fully conditional and depends only on the returns of basic assets. Return data for several economies reveal that RMP is...

We show how distributions can be reduced to low-dimensional scenario trees. Applied to intertemporal distributions, the scenarios and their probabilities become time-varying factors. From S&P 500 options, two or three time-varying scenarios suffice to forecast returns, implied variance or...

We investigate the market-compatible degree of agent heterogeneity by identifying and analyzing the full range of conditional beliefs consistent with observed asset prices and good-deal bounds. Our methodology neither makes assumptions on underlying processes nor does it use survey data. It can...

This paper develops an optimal trading strategy explicitly linked to an agent's preferences and assessment of the distribution of asset returns. The price of this strategy is a portfolio of implied moments, and its expected excess returns naturally accommodate compensation for higher-order...