The Distribution of Sums of Certain I.I.D. Pareto Variates

ABSTRACT

Though the Pareto distribution is important to actuaries and economists, an exact expression for the distribution of the sum of n i.i.d. Pareto variates has been difficult to obtain in general. This article considers Pareto random variables with common probability density function (pdf) f(x) = (α/β) (1 + x/β)^α+1 for x > 0, where α = 1,2,… and β > 0 is a scale parameter. To date, explicit expressions are known only for a few special cases: (i) α = 1 and n = 1,2,3; (ii) 0 < α < 1 and n = 1,2,…; and (iii) 1 < α < 2 and n = 1,2,…. New expressions are provided for the more general case where β > 0, and α and n are positive integers. Laplace transforms and generalized exponential integrals are used to derive these expressions, which involve integrals of real valued functions on the positive real line. An important attribute of these expressions is that the integrands involved are non oscillating.     

Search With Adverse Selection

This paper analyzes a sequential search model with adverse selection. We study information aggregation by the price—how close the equilibrium prices are to the full‐information prices—when search frictions are small. We identify circumstances under which prices fail to aggregate information well even when search frictions are small. We trace this to a strong form of the winner's curse that is present in the sequential search model. The failure of information aggregation may result in inefficient allocations.     

Business Angel Investment as an Informal Learning Process: Does Experience Matter?

This paper addresses the question of how the informal learning processes of angel investors shape the way in which they assess new investment opportunities. Previous research has suggested that angels learn from their previous investment activity. However, the measurement of investment experience as a function of years of investing and number of investments made does not take into account how, and to what extent, learning occurs and how it impacts investors’ decision-making. To address this deficiency, we suggest a dynamic model of informal learning which incorporates the informal learning typology developed by Schugurensky and extended by Bennett, as a conceptual framework to understand how learning experiences impact angel investment decisions. Based on interviews and verbal protocol analysis with 30 investors, we demonstrate how learning impacts learning processes and outcomes as angels assess an investment opportunity. The findings highlight the importance of supporting angel learning with support for angel groups and angel training programmes.