A Stochastic Bioeconomic Model with Research

This paper provides an incremental extension of a stochastic renewable resource model (Pindyck 1984) to include population dynamics research; i.e., the rate of accrual of information regarding the stochastic evolution of the stock, as a dynamic choice variable. While Pindyck models variance in stock growth as an exogenous parameter, our formulation endogenizes this variance and characterizes the impact of scientific information accrual on both the harvest decision and the present value of rents resulting from harvest activity. We illustrate the theoretical existence of an internal optimum in research effort using a numerical example.stochastic bioeconomic model, stochastic control, fisheries management, population dynamics research, renewable resource, uncertainty, Resource /Energy Economics and Policy, Q2, Q22, C61,

Online learning in repeated auctions

Motivated by online advertising auctions, we consider repeated Vickrey auctions where goods of unknown value are sold sequentially and bidders only learn (potentially noisy) information about a good's value once it is purchased. We adopt an online learning approach with bandit feedback to model this problem and derive bidding strategies for two models: stochastic and adversarial. In the stochastic model, the observed values of the goods are random variables centered around the true value of the good. In this case, logarithmic regret is achievable when competing against well behaved adversaries. In the adversarial model, the goods need not be identical and we simply compare our performance against that of the best fixed bid in hindsight. We show that sublinear regret is also achievable in this case and prove matching minimax lower bounds. To our knowledge, this is the first complete set of strategies for bidders participating in auctions of this type

Forecasting stochastic Volatility using the Kalman filter: An Application to Canadian Interest Rates and Price-Earnings Ratio

In this paper, we aim at forecasting the stochastic volatility of key financial market variables with the Kalman filter using stochastic models developed by Taylor (1986, 1994) and Nelson (1990). First, we compare a stochastic volatility model relying on the Kalman filter to the conditional volatility estimated with the GARCH model. We apply our models to Canadian short-term interest rates. When comparing the profile of the interest rate stochastic volatility to the conditional one, we find that the omission of a constant term in the stochastic volatility model might have a perverse effect leading to a scaling problem, a problem often overlooked in the literature. Stochastic volatility seems to be a better forecasting tool than GARCH(1,1) since it is less conditioned by autoregressive past information. Second, we filter the S&P500 price-earnings (P/E) ratio in order to forecast its value. To make this forecast, we postulate a rational expectations process but our method may accommodate other data generating processes. We find that our forecast is close to a GARCH(1,1) profile.Stochastic volatility; Kalman filter; P/E ratio forecast; Interest rate forecast.