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作者：Chang, Mou-Hsiung; Pang, Tao; Yang, Yipeng
作者单位：North Carolina State University; University of Missouri System; University of Missouri Columbia
摘要：This paper considers a portfolio management problem of Merton's type in which the risky asset return is related to the return history. The problem is modeled by a stochastic system with delay. The investor's goal is to choose the investment control as well as the consumption control to maximize his total expected, discounted utility. Under certain situations, we derive the explicit solutions in a finite dimensional space.
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作者：Deng, Xiaotie; Qi, Qi; Saberi, Amin; Zhang, Jie
作者单位：University of Liverpool; Stanford University; City University of Hong Kong
摘要：We study three discrete fixed point concept (SPERNER, DPZP, BROUWER) under two different models: the polynomial-time function model and the oracle function model. We fully characterize the computational complexities of these three problems. The computational complexity unification of the above problems gives us more choices in the study of different applications. As an example, by a reduction from DPZP, we derive asymptotically equal lower and upper bound for TUCKER in the oracle model. The sa...
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作者：Nie, Jiawang
作者单位：University of California System; University of California San Diego
摘要：Consider a convex set S = {x is an element of D: G(x) >= 0}, where G(x) is a symmetric matrix whose every entry is a polynomial or rational function, D subset of R-n is a domain on which G(x) is defined, and G(x) >= 0 means G(x) is positive semidefinite. The set S is called semidefinite representable if it equals the projection of a higher dimensional set that is defined by a linear matrix inequality (LMI). This paper studies sufficient conditions guaranteeing semidefinite representability of ...
