This paper examines the theory of commercial mortgage default and tests it using a data set of 2,899 loan histories provided by a major multi-line insurance company. A default model is estimated which relates subsequent default incidence and timing to contemporaneous loan term, borrower, property and economic/market conditions. Maximum likelihood estimation is used to estimate a hazard function predicting conditional probability of default over time. Results confirm many expected default relationships, in particular the dominance of loan terms and property value trends over time in affecting default. The effectiveness of the model in discriminating between "good" and "bad" loans is explored. Implications for underwriting practice and credit risk diversification are noted. Finally, suggestions are made for extending these results in pricing applications. Copyright American Real Estate and Urban Economics Association.

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In this paper we investigate the computational complexity of motivating time-inconsistent agents to complete long term projects. We resort to an elegant graph-theoretic model, introduced by Kleinberg and Oren [4], which consists of a task graph G with n vertices, including a source s and target t, and an agent that incrementally constructs a path from s to t in order to collect rewards. The twist is that the agent is present-biased and discounts future costs and rewards by a factor β ∈ [0, 1]. Our design objective is to ensure that the agent reaches t i.e. completes the project, for as little reward as possible. Such graphs are called motivating. We consider two strategies.First, we place a single reward r at t and try to guide the agent by removing edges from G. We prove that deciding the existence of such motivating subgraphs is NP-complete if r is fixed. More importantly, we generalize our reduction to a hardness of approximation result for computing the minimum r that admits a motivating subgraph. In particular, we show that no polynomial-time approximation to within a ratio of √ n/4 or less is possible, unless P = NP. Furthermore, we develop a (1 + √ n)-approximation algorithm and thus settle the approximability of computing motivating subgraphs. Secondly, we study motivating reward configurations, where non-negative rewards r(v) may be placed on arbitrary vertices v of G. The agent only receives the rewards of visited vertices. Again we give an NPcompleteness result for deciding the existence of a motivating reward configuration within a fixed budget b. This result even holds if b = 0, which in turn implies that no efficient approximation of a minimum b within a ration grater or equal to 1 is possible, unless P = NP. * or postpone it to the next day. However, the longer she waits, the dirtier the car gets. Assume that washing the car on day i, with i ≥ 1, incurs a cost of i/50. The cost of waiting another day is 0. After completion of the task, she will receive a reward of 1 Euro from the family. Alice is present-biased, i.e. she perceives current cost according to its true value but discounts future costs and rewards by a factor of β ∈ [0, 1]. On day i she compares the cost of washing the car right away, which is i/50, to the perceived cost of washing it on the next day, which is β(i + 1)/50. Suppose that β = 1/3. Because i/50 > β(i + 1)/50, she procrastinates with good intentions of doing the job on the following day. On day i = 50 Alice realizes that her perceived cost for washing the car on the next day, or any of the following days, is at least β(50 + 1)/50, which exceeds the perceived value of β. Thus she abandons the project altogether.Previous work: In the economic literature there exists a considerable body of work on time-inconsistent behavior, cf. again [1,7,8]. We build on work by Kleinberg and Oren [4] who propose a graph-theoretic model that elegantly captures the phenomena of procrastination and abandonment as observed in the car wash problem. We will formally define the model in Section 2. ...

Abstract. The tendency to overestimate immediate utility is a common cognitive bias. As a result people behave inconsistently over time and fail to reach long-term goals. Behavioral economics tries to help affected individuals by implementing external incentives. However, designing robust incentives is often difficult due to imperfect knowledge of the parameter β ∈ (0, 1] quantifying a person's present bias. Using the graphical model of Kleinberg and Oren [8], we approach this problem from an algorithmic perspective. Based on the assumption that the only information about β is its membership in some set B ⊂ (0, 1], we distinguish between two models of uncertainty: one in which β is fixed and one in which it varies over time. As our main result we show that the conceptual loss of efficiency incurred by incentives in the form of penalty fees is at most 2 in the former and 1 + max B/ min B in the latter model. We also give asymptotically matching lower bounds and approximation algorithms.

Abstract. Approximating the optimal social welfare while preserving truthfulness is a well studied problem in algorithmic mechanism design. Assuming that the social welfare of a given mechanism design problem can be optimized by an integer program whose integrality gap is at most α, Lavi and Swamy [1] propose a general approach to designing a randomized α-approximation mechanism which is truthful in expectation. Their method is based on decomposing an optimal solution for the relaxed linear program into a convex combination of integer solutions. Unfortunately, Lavi and Swamy's decomposition technique relies heavily on the ellipsoid method, which is notorious for its poor practical performance. To overcome this problem, we present an alternative decomposition technique which yields an α(1 + ǫ) approximation and only requires a quadratic number of calls to an integrality gap verifier.