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Convex Analysisの二,三の進展について

Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

Continuous-time stochastic control and optimization with financial applications / Huyen Pham

Small and Medium‐Sized Enterprises (SMEs) face tremendous challenges in their attempt to pursue technological innovations. This paper argues that co‐opetition strategy—simultaneous pursuit of compe...

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Co-opetition and Technological Innovation in Small and Medium-Sized Enterprises: A Multilevel Conceptual Model

We survey the economic literature, both theoretical and empirical, on the choice of intellectual property protection by firms. Our focus is on the trade-offs between using patents and disclosing versus the use of secrecy, although we also look briefly at the use of other means of formal intellectual property protection.

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The Choice between Formal and Informal Intellectual Property: A Review

We examine a market in which long-lived firms face a short-term incentive to exert low effort, but could earn higher profits if it were possible to commit to high effort. There are two types of firms, "inept" firms who can only exert low effort, and "competent" firms who have a choice between high and low effort. There is occasional exit, and competent and inept potential entrants compete for the right to inherit the departing firm's reputation. Consumers receive noisy signals of effort choice, and so competent firms choose high effort in an attempt to distinguish themselves from inept firms. A competent firm is most likely to enter the market by purchasing an average reputation, in the hopes of building it into a good reputation, than either a very low reputation or a very high reputation. Inept firms, in contrast, find it more profitable to either buy high reputations and deplete them or buy low reputations.

Who wants a good reputation

We study mechanism design in dynamic quasilinear environments where private information arrives over time and decisions are made over multiple periods. We make three contributions. First, we provide a necessary condition for incentive compatibility that takes the form of an envelope formula for the derivative of an agent's equilibrium expected payoff with respect to his current type. It combines the familiar marginal effect of types on payoffs with novel marginal effects of the current type on future ones that are captured by �impulse response functions.� The formula yields an expression for dynamic virtual surplus that is instrumental to the design of optimal mechanisms and to the study of distortions under such mechanisms. Second, we characterize the transfers that satisfy the envelope formula and establish a sense in which they are pinned down by the allocation rule (�revenue equivalence�). Third, we characterize perfect Bayesian equilibrium-implementable allocation rules in Markov environments, which yields tractable sufficient conditions that facilitate novel applications. We illustrate the results by applying them to the design of optimal mechanisms for the sale of experience goods (�bandit auctions�).

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Dynamic Mechanism Design: A Myersonian Approach

We develop an equilibrium search model of innovation with the possibility of multiple independent discovery. We distinguish innovations from ideas, and we view patents as probabilistic property rights that are constrained by the innovators' option to keep the innovation secret. We find that the patent system can simultaneously stimulate innovation, information disclosure and welfare. An optimal patent may provide more or less protection than secrecy, and in many cases, it provides less, suggesting that its main function is information spreading rather than rewarding the costs of the innovative activity.

Secrecy versus patenting

We examine the design of incentive-compatible screening mechanisms for dynamic environ- ments in which the agents'types follow a (possibly non-Markov) stochastic process, decisions may be made over time and may aect the type process, and payos need not be time-separable. We derive a formula for the derivative of an agent's equilibrium payowith respect to his cur- rent type in an incentive-compatible mechanism, which summarizes all …rst-order conditions for incentive compatibility and generalizes Mirrlees's envelope formula of static mechanism design. We provide conditions on the environment under which this formula must hold in any incentive- compatible mechanism. When specialized to quasi-linear environments, this formula yields a dynamic "revenue-equivalence"result and an expression for dynamic virtual surplus, which is instrumental for the design of optimal mechanisms. We also provide some su¢ cient conditions for incentive compatibility, and for its robustness to an agent's observation of the other agents' past and future types. We apply these results to a number of novel settings, including the de- sign of pro…t-maximizing auctions and durable-good selling mechanisms for buyers whose values

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Dynamic Mechanism Design: Incentive Compatibility, Pro…t Maximization and Information Disclosure

Multiple innovators can and do come up with the same invention independently. A famous case is the telephone: two hours after Alexander Graham Bell filed a patent application for it, another application for the same invention arrived at the patent office. Many scholars, such as Ilkka Rahnasto (2003) and Hal R. Varian et al. (2004), argue that since Bell’s time, simultaneous innovation has become increasingly common. We feel, and our discussions with industry practitioners confirm, that the simultaneous model of innovation characterizes especially network industries such as consumer electronics, the Internet, software, telecommunications, and payment systems, where standardization limits the possible paths for future technologies and so firms concentrate their R&D activities on the same fields. We suggest that simultaneous or independent invention has major implications for intellectual property (IP) policy. In particular, the possibility of simultaneous innovation changes the patenting decision: firms tap patents for a defensive purpose, since the choice is no longer between patenting or resorting to trade secrecy, but between patenting or letting competitors patent. By exploiting the vulnerability of innovative firms to rival innovation, it is possible to design a welfareimproving patent system that induces innovators to patent rather than keep their innovations secret. Taking the simultaneous nature of innovation seriously also changes the way one should think about the relationship between IP and competition policies.

Simultaneous Model of Innovation, Secrecy, and Patent Policy

We study repeated Bayesian games with communication and observable actions in which the players' privately known payoffs evolve according to an irreducible Markov chain whose transitions are independent across players. Our main result implies that, generically, any Pareto-efficient payoff vector above a stationary minmax value can be approximated arbitrarily closely in a perfect Bayesian equilibrium as the discount factor goes to 1. As an intermediate step, we construct an approximately efficient dynamic mechanism for long finite horizons without assuming transferable utility. [PUBLICATION ABSTRACT]

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Juuso Toikka

Papers

Dynamic Mechanism Design: A Myersonian Approach

Secrecy versus patenting

Dynamic Mechanism Design: Incentive Compatibility, Pro…t Maximization and Information Disclosure

Simultaneous Model of Innovation, Secrecy, and Patent Policy

Efficiency in Games With Markovian Private Information