Optimal long term investment model with memory

We consider a financial market model driven by an R^n-valued Gaussian process with stationary increments which is different from Brownian motion. This driving noise process consists of $n$ independent components, and each component has memory described by two parameters. For this market model, we explicitly solve optimal investment problems. These include (i) Merton's portfolio optimization problem; (ii) the maximization of growth rate of expected utility of wealth over the infinite horizon; (iii) the maximization of the large deviation probability that the wealth grows at a higher rate than a given benchmark. The estimation of paremeters is also considered.Comment: 25 pages, 3 figures. To appear in Applied Mathematics and Optimizatio

Binary market models with memory

We construct a binary market model with memory that approximates a continuous-time market model driven by a Gaussian process equivalent to Brownian motion. We give a sufficient conditions for the binary market to be arbitrage-free. In a case when arbitrage opportunities exist, we present the rate at which the arbitrage probability tends to zero as the number of periods goes to infinity.Comment: 13 page

Linear filtering of systems with memory

We study the linear filtering problem for systems driven by continuous Gaussian processes with memory described by two parameters. The driving processes have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. It allows for straightforward parameter estimations. After giving the semimartingale representations of the processes by innovation theory, we derive Kalman-Bucy-type filtering equations for the systems. We apply the result to the optimal portfolio problem for an investor with partial observations. We illustrate the tractability of the filtering algorithm by numerical implementations.Comment: Full names are use

Sulfuric acid as a cryofluid and oxygen isotope reservoir of planetesimals

The Sun exhibits a depletion in $^{17,18}$O relative to $^{16}$O by 6 % compared to the Earth and Moon$^{1}$. The origin of such a non-mass-dependent isotope fractionation has been extensively debated since the three-isotope-analysis$^{2}$ became available in 1970's. Self-shielding$^{3,4}$ of CO molecules against UV photons in the solar system's parent molecular cloud has been suggested as a source of the non-mass-dependent effect, in which a $^{17,18}$O-enriched oxygen was trapped by ice and selectively incorporated as water into planet-forming materials$^{5}$. The truth is that the Earth-Moon and other planetary objects deviate positively from the Sun by ~6 % in their isotopic compositions. A stunning exception is the magnetite/sulfide symplectite found in Acfer 094 meteorite, which shows 24 % enrichment in $^{17,18}$O relative to the Sun$^{6}$. Water does not explain the enrichment this high. Here we show that the SO and SO$_2$ molecules in the molecular cloud, ~106 % enriched in $^{17,18}$O relative to the Sun, evolved through the protoplanetary disk and planetesimal stages to become a sulfuric acid, 24 % enriched in $^{17,18}$O. The sulfuric acid provided a cryofluid environment in the planetesimal and by itself reacted with ferric iron to form an amorphous ferric-hydroxysulfate-hydrate, which eventually decomposed into the symplectite by shock. We indicate that the Acfer-094 symplectite and its progenitor, sulfuric acid, is strongly coupled with the material evolution in the solar system since the days of our molecular cloud.Comment: 19 pages, 3 figure

Remark on optimal investment in a market with memory

We consider a financial market model driven by a Gaussian semimartingale with stationary increments. This driving noise process consists of independent components and each component has memory described by two parameters. We extend results of the authors on optimal investment in this market

Phase structure of topological insulators by lattice strong-coupling expansion

The effect of the strong electron correlation on the topological phase structure of 2-dimensional (2D) and 3D topological insulators is investigated, in terms of lattice gauge theory. The effective model for noninteracting system is constructed similarly to the lattice fermions with the Wilson term, corresponding to the spin-orbit coupling. Introducing the electron-electron interaction as the coupling to the gauge field, we analyze the behavior of emergent orders by the strong coupling expansion methods. We show that there appears a new phase with the in-plane antiferromagnetic order in the 2D topological insulator, which is similar to the so-called "Aoki phase" in lattice QCD with Wilson fermions. In the 3D case, on the other hand, there does not appear such a new phase, and the electron correlation results in the shift of the phase boundary between the topological phase and the normal phase.Comment: 7 pages, 2 figures; Presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German