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The learning premium. (English) Zbl 1469.91048

The authors developed a model for asset pricing. To identify the posterior distributions at each time, they observed that these distributions coincide with those arising from a Pólya urn scheme, and hence yield posteriors in the beta-binomial class. Then they find in closed form the stock price and its implied equilibrium rate when the representative investor has time-additive utility. In this case, they investigated the recursive preferences of L. G. Epstein and S. E. Zin [Econometrica 57, No. 4, 937–969 (1989; Zbl 0683.90012)].
The model is based on a Lucas’s tree economy with one unit of a risky asset (see for example (see [R. E. Lucas jun., Econometrica 46, 1429–1445 (1978; Zbl 0398.90016)] or [I. Martin, Econometrica 81, No. 1, 55–111 (2013; Zbl 1274.91202)]), which yields at time \(t\) a perishable dividend \(D_t\) that starts at \(D_0\) and follows a discrete-time process.
The main result identifies the price-divide ratio and safe rate in equilibrium over time and is given in Theorem 4.1.

MSC:

91G10 Portfolio theory
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