Investment Under Uncertainty and Time-Inconsistent Preferences

The real options framework has been used extensively to analyze the timing of investment under uncertainty. While standard real options models assume that agents possess a constant rate of time preference, there is substantial evidence that agents are very impatient about choices in the short-term, but are quite patient when choosing between long-term alternatives. We extend the real options framework to model the investment timing decisions of entrepreneurs with such time-inconsistent preferences. Two opposing forces determine investment timing: while evolving uncertainty induces entrepreneurs to defer investment in order to take advantage of the option to wait, their time-inconsistent preferences motivate them to invest earlier in order to avoid the time-inconsistent behavior they will display in the future. We find that the precise trade-off between these two forces depends on such factors as whether entrepreneurs are sophisticated or naive in their expectations regarding their future time-inconsistent behavior, as well as whether the payoff from investment occurs all at once or over time. We extend the model to consider equilibrium investment behavior for an industry comprised of time-inconsistent entrepreneurs. Such an equilibrium involves the dual problem of entrepreneurs playing dynamic games against competitors as well as against their own future selves.

Pension Contribution as a Commitment Device: Evidence of Sophistication among Time-inconsistent Households

Sophisticated agents with self-control problems value commitment devices that constrain future choices. Using Australian household data I test whether these households value commitment devices in the form of illiquid pension contributions. Applying various probabilistic choice models, the results confirm the conjecture that households with problems of self-control are more likely to invest in illiquid pensions while less likely to hold very liquid forms of assets.

Pension Contributions as a Commitment device: evidence of sophistication among time-inconsistent households

Sophisticated agents with self-control problems value commitment devices that constrain future choices. Using Australian household data, I test whether these households value commitment devices in the form of illiquid pension contributions. Applying various probabilistic choice models, the results confirm the conjecture that households with problems of self-control are more likely to invest in illiquid pensions while less likely to hold very liquid forms of assets.commitment device; pensions; intertemporal choice

Ramsey Rule with Progressive utility and Long Term Affine Yields Curves

The purpose of this paper relies on the study of long term affine yield curves modeling. It is inspired by the Ramsey rule of the economic literature, that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new economic information is crucial, justifying the use of progressive utility. This paper studies, in a framework with affine factors, the yield curve given from the Ramsey rule. It first characterizes consistent progressive utility of investment and consumption, given the optimal wealth and consumption processes. A special attention is paid to utilities associated with linear optimal processes with respect to their initial conditions, which is for example the case of power progressive utilities. Those utilities are the basis point to construct other progressive utilities generating non linear optimal processes but leading yet to still tractable computations. This is of particular interest to study the impact of initial wealth on yield curves.Comment: arXiv admin note: substantial text overlap with arXiv:1404.189

Utility based pricing of contingent claims

In a discrete setting, we develop a model for pricing a contingent claim. Since the presence of hedging opportunities influences the price of a contingent claim, first we introduce the optimal hedging strategy assuming a contingent claim has been issued: a strategy implemented by investing the budget plus the selling price is optimal if it maximizes the expected utility of the agent's revenue, which is the difference between the outcome of the hedging portfolio and the payoff of the claim. Next, we introduce the `reservation price' as a subjective valuation of a contingent claim. This is defined as the minimum price to be added to the initial budget that makes the issue of the claim more preferable than optimally investing in the available securities. We define the reservation price both for a short position (reservation selling price) and for a long position (reservation buying price) in the contingent claim. When the contingent claim is redundant, both the selling and the buying price collapse in the usual Arrow-Debreu price. We develop a numerical procedure to evaluate the reservation price and two applications are provided. Different utility functions are used and some qualitative properties of the reservation price are shown.Incomplete markets, reservation price, expected utility, optimization

Equilibria for Time-inconsistent Singular Control Problems

We study a time-inconsistent singular control problem originating from irreversible reinsurance decisions with non-exponential discount. Novel definitions of weak and strong equilibria for time-inconsistent singular control problems are introduced. For the problem with non-exponential discount, both sufficient and necessary conditions are derived, providing a thorough mathematical characterization of both equilibria. In particular, the weak equilibrium can be characterized by an extended HJB system, which is a coupled system of non-local parabolic equations with free boundaries. Finally, by showing the existence of classical solutions to the extended HJB system, the existence of weak equilibrium is established under some additional assumptions

Stability of Radner Equilibria with respect to small frictions

We study risk-sharing equilibria with trading subject to small proportional transaction costs. We show that the frictionless equilibrium prices also form an "asymptotic equilibrium" in the small-cost limit. To wit, there exist asymptotically optimal policies for all agents and a split of the trading cost according to their risk aversions for which the frictionless equilibrium prices still clear the market. Starting from a frictionless equilibrium, this allows to study the interplay of volatility, liquidity, and trading volume