This paper characterizes the optimal first-price auction (FPA) and second-price auction (SPA) for selling rights, contracts, or licenses that involve ensuing payoff uncertainty for the winning bidder. The distribution of the random payoff is common knowledge, except that bidders have private...

We present an accurate and efficient method for Bayesian forecasting of two financial risk measures, Value-at-Risk and Expected Shortfall, for a given volatility model. We obtain precise forecasts of the tail of the distribution of returns not only for the 10-days-ahead horizon required by the...

In recent years the Value at Risk (VaR) concept for measuringdownside risk has been widelystudied. VaR basically is a summary statistic that quantifies theexposure of an asset or portfolio tomarket risk, or the risk that a position declines in value withadverse market price changes. Threeparties...