Owner-managers of private companies are often highly underdiversified. We investigate the consequences of underdiversification at the company level. There is a strong positive relationship between underdiversification, measured as the share of personal net worth invested in the company, and profitability, measured as the return on equity. The analysis identifies two causes for this underdiversi...

An information transaction entails the purchase of information. Formally, it consists of an information structure together with a price. We develop an index of the appeal of information transactions, which is derived as a dual to the agent’s preferences for information. The index of information transactions has a simple analytic characterization in terms of the relative entropy from priors to p...

We consider a stochastic model for a defined-contribution pension fund in continuous time. In particular, we focus on the portfolio problem of a fund manager who wants to maximize the expected utility of his terminal wealth in a complete financial market with stochastic interest rate. The fund manager must cope with a set of stochastic investment opportunities and two background risks: the sala...

In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e. a least favorable frictionless market leading to the same optimal strategy and utility as in the original market under transaction costs. The crucial ingredi...

We use unique institutional securities holdings data to examine the trading behaviour of delegated capital and its impact on bond risk premia. show that fund managers trade strongly procyclically: they actively move into higher yielding, longer duration lower rated as yields fall spreads compress, vice versa. Funds more exposed negative increase their risk-taking strongly, this effect is partic...

In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volume. At the first order, the liquidity premium equals the spread, times share ...

For portfolio optimisation under proportional transaction costs, we provide a duality theory for general càdlàg price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised sense. This shadow price is defined via a “sandwiched” process consisting of a predictable and an optional strong supermartingale and pertains to all strateg...

The present paper accomplishes a major step towards a reconciliation of two conflicting approaches in mathematical finance: on the one hand, the mainstream approach based on the notion of no arbitrage (Black, Merton & Scholes); and on the other hand, the consideration of non-semimartingale price processes, the archetype of which being fractional Brownian motion (Mandelbrot). Imposing (arbitrari...

This paper deals with a constrained investment problem for a defined contribution (DC) pension fund where retirees are allowed to defer the purchase of the annuity at some future time after retirement. This problem has already been treated in the unconstrained case in a number of papers. The aim of this work is to deal with the more realistic case when constraints on the investment strategies a...