3,345 research outputs found
Impact of Seismic Risk on Lifetime Property Values
This report presents a methodology for establishing the uncertain net asset value, NAV, of a real-estate investment opportunity considering both market risk and seismic risk for the property. It also presents a decision-making procedure to assist in making real-estate investment choices under conditions of uncertainty and risk-aversion. It is shown that that market risk, as measured by the coefficient of variation of NAV, is at least 0.2 and may exceed 1.0. In a situation of such high uncertainty, where potential gains and losses are large relative to a decision-maker's risk tolerance, it is appropriate to adopt a decision-analysis approach to real-estate investment decision-making. A simple equation for doing so is presented. The decision-analysis approach uses the certainty equivalent, CE, as opposed to NAV as the basis for investment decision-making. That is, when faced with multiple investment alternatives, one should choose the alternative that maximizes CE. It is shown that CE is less than the expected value of NAV by an amount proportional to the variance of NAV and the inverse of the decision-maker's risk tolerance, [rho].
The procedure for establishing NAV and CE is illustrated in parallel demonstrations by CUREE and Kajima research teams. The CUREE demonstration is performed using a real 1960s-era hotel building in Van Nuys, California. The building, a 7-story non-ductile reinforced-concrete moment-frame building, is analyzed using the assembly-based vulnerability (ABV) method, developed in Phase III of the CUREE-Kajima Joint Research Program. The building is analyzed three ways: in its condition prior to the 1994 Northridge Earthquake, with a hypothetical shearwall upgrade, and with earthquake insurance. This is the first application of ABV to a real building, and the first time ABV has incorporated stochastic structural analyses that consider uncertainties in the mass, damping, and force-deformation behavior of the structure, along with uncertainties in ground motion, component damageability, and repair costs. New fragility functions are developed for the reinforced concrete flexural members using published laboratory test data, and new unit repair costs for these components are developed by a professional construction cost estimator. Four investment alternatives are considered: do not buy; buy; buy and retrofit; and buy and insure. It is found that the best alternative for most reasonable values of discount rate, risk tolerance, and market risk is to buy and leave the building as-is. However, risk tolerance and market risk (variability of income) both materially affect the decision. That is, for certain ranges of each parameter, the best investment alternative changes. This indicates that expected-value decision-making is inappropriate for some decision-makers and investment opportunities. It is also found that the majority of the economic seismic risk results from shaking of S[subscript a] < 0.3g, i.e., shaking with return periods on the order of 50 to 100 yr that cause primarily architectural damage, rather than from the strong, rare events of which common probable maximum loss (PML) measurements are indicative.
The Kajima demonstration is performed using three Tokyo buildings. A nine-story, steel-reinforced-concrete building built in 1961 is analyzed as two designs: as-is, and with a steel-braced-frame structural upgrade. The third building is 29-story, 1999 steel-frame structure. The three buildings are intended to meet collapse-prevention, life-safety, and operational performance levels, respectively, in shaking with 10%exceedance probability in 50 years. The buildings are assessed using levels 2 and 3 of Kajima's three-level analysis methodology. These are semi-assembly based approaches, which subdivide a building into categories of components, estimate the loss of these component categories for given ground motions, and combine the losses for the entire building. The two methods are used to estimate annualized losses and to create curves that relate loss to exceedance probability. The results are incorporated in the input to a sophisticated program developed by the Kajima Corporation, called Kajima D, which forecasts cash flows for office, retail, and residential projects for purposes of property screening, due diligence, negotiation, financial structuring, and strategic planning. The result is an estimate of NAV for each building. A parametric study of CE for each building is presented, along with a simplified model for calculating CE as a function of mean NAV and coefficient of variation of NAV. The equation agrees with that developed in parallel by the CUREE team.
Both the CUREE and Kajima teams collaborated with a number of real-estate investors to understand their seismic risk-management practices, and to formulate and to assess the viability of the proposed decision-making methodologies. Investors were interviewed to elicit their risk-tolerance, r, using scripts developed and presented here in English and Japanese. Results of 10 such interviews are presented, which show that a strong relationship exists between a decision-maker's annual revenue, R, and his or her risk tolerance, [rho is approximately equal to] 0.0075R[superscript 1.34]. The interviews show that earthquake risk is a marginal consideration in current investment practice. Probable maximum loss (PML) is the only earthquake risk parameter these investors consider, and they typically do not use seismic risk at all in their financial analysis of an investment opportunity. For competitive reasons, a public investor interviewed here would not wish to account for seismic risk in his financial analysis unless rating agencies required him to do so or such consideration otherwise became standard practice. However, in cases where seismic risk is high enough to significantly reduce return, a private investor expressed the desire to account for seismic risk via expected annualized loss (EAL) if it were inexpensive to do so, i.e., if the cost of calculating the EAL were not substantially greater than that of PML alone.
The study results point to a number of interesting opportunities for future research, namely: improve the market-risk stochastic model, including comparison of actual long-term income with initial income projections; improve the risk-attitude interview; account for uncertainties in repair method and in the relationship between repair cost and loss; relate the damage state of structural elements with points on the force-deformation relationship; examine simpler dynamic analysis as a means to estimate vulnerability; examine the relationship between simplified engineering demand parameters and performance; enhance category-based vulnerability functions by compiling a library of building-specific ones; and work with lenders and real-estate industry analysts to determine the conditions under which seismic risk should be reflected in investors' financial analyses
Bethe Ansatz Equations for the Broken -Symmetric Model
We obtain the Bethe Ansatz equations for the broken -symmetric
model by constructing a functional relation of the transfer matrix of
-operators. This model is an elliptic off-critical extension of the
Fateev-Zamolodchikov model. We calculate the free energy of this model on the
basis of the string hypothesis.Comment: 43 pages, latex, 11 figure
Logarithmic perturbation theory for quasinormal modes
Logarithmic perturbation theory (LPT) is developed and applied to quasinormal
modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is
especially convenient because summation over a complete set of unperturbed
states is not required. Attention is paid to potentials with exponential tails,
and the example of a Poschl-Teller potential is briefly discussed. A numerical
method is developed that handles the exponentially large wavefunctions which
appear in dealing with QNMs.Comment: 24 pages, 4 Postscript figures, uses ioplppt.sty and epsfig.st
Determination of hadronic partial widths for scalar-isoscalar resonances f0(980), f0(1300), f0(1500), f_0(1750) and the broad state f0(1530^{+90}_{-250})
In the article of V.V. Anisovich et al., Yad. Fiz. 63, 1489 (2000), the
K-matrix solutions for the wave IJ^{PC}=00^{++} were obtained in the mass
region 450 - 1900 MeV where four resonances f0(980), f0(1300), f0(1500),
f0(1750) and the broad state f0(1530^{+90}_{-250}) are located. Based on these
solutions, we determine partial widths for scalar-isoscalar states decaying
into the channels pi-pi, K-anti K, eta-eta, eta-eta', pi-pi-pi-pi and
corresponding decay couplings.Comment: Some typos were correcte
Three-Dimensional Vertex Model in Statistical Mechanics, from Baxter-Bazhanov Model
We find that the Boltzmann weight of the three-dimensional Baxter-Bazhanov
model is dependent on four spin variables which are the linear combinations of
the spins on the corner sites of the cube and the Wu-Kadanoff duality between
the cube and vertex type tetrahedron equations is obtained explicitly for the
Baxter-Bazhanov model. Then a three-dimensional vertex model is obtained by
considering the symmetry property of the weight function, which is
corresponding to the three-dimensional Baxter-Bazhanov model. The vertex type
weight function is parametrized as the dihedral angles between the rapidity
planes connected with the cube. And we write down the symmetry relations of the
weight functions under the actions of the symmetry group of the cube. The
six angles with a constrained condition, appeared in the tetrahedron equation,
can be regarded as the six spectrums connected with the six spaces in which the
vertex type tetrahedron equation is defined.Comment: 29 pages, latex, 8 pasted figures (Page:22-29
Effect of Gravity and Confinement on Phase Equilibria: A Density Matrix Renormalization Approach
The phase diagram of the 2D Ising model confined between two infinite walls
and subject to opposing surface fields and to a bulk "gravitational" field is
calculated by means of density matrix renormalization methods. In absence of
gravity two phase coexistence is restricted to temperatures below the wetting
temperature. We find that gravity restores the two phase coexistence up to the
bulk critical temperature, in agreement with previous mean-field predictions.
We calculate the exponents governing the finite size scaling in the temperature
and in the gravitational field directions. The former is the exponent which
describes the shift of the critical temperature in capillary condensation. The
latter agrees, for large surface fields, with a scaling assumption of Van
Leeuwen and Sengers. Magnetization profiles in the two phase and in the single
phase region are calculated. The profiles in the single phase region, where an
interface is present, agree well with magnetization profiles calculated from a
simple solid-on-solid interface hamiltonian.Comment: 4 pages, RevTeX and 4 PostScript figures included. Final version as
published. To appear in Phys. Rev. Let
Factorized finite-size Ising model spin matrix elements from Separation of Variables
Using the Sklyanin-Kharchev-Lebedev method of Separation of Variables adapted
to the cyclic Baxter--Bazhanov--Stroganov or -model, we derive
factorized formulae for general finite-size Ising model spin matrix elements,
proving a recent conjecture by Bugrij and Lisovyy
Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
The antiperiodic transfer matrix associated to higher spin representations of
the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the
approach introduced recently in [1], for the cyclic representations, in [2],
for the spin-1/2 highest weight representations, and in [3], for the spin 1/2
representations of the reflection algebra. Here, we derive the complete
characterization of the transfer matrix spectrum and we prove its simplicity in
the framework of Sklyanin's quantum separation of variables (SOV). Then, the
characterization of local operators by Sklyanin's quantum separate variables
and the expression of the scalar products of separates states by determinant
formulae allow to compute the form factors of the local spin operators by one
determinant formulae similar to the scalar product ones. Finally, let us
comment that these results represent the SOV analogous in the antiperiodic
higher spin XXX quantum chains of the results obtained for the periodic chains
in [4] in the framework of the algebraic Bethe ansatz.Comment: 20 pages, introduction improved by taking into account some relevant
references on the spectrum of the model under general boundary conditions, no
further relevant modification
Semiclassical treatment of logarithmic perturbation theory
The explicit semiclassical treatment of logarithmic perturbation theory for
the nonrelativistic bound states problem is developed. Based upon
-expansions and suitable quantization conditions a new procedure for
deriving perturbation expansions for the one-dimensional anharmonic oscillator
is offered. Avoiding disadvantages of the standard approach, new handy
recursion formulae with the same simple form both for ground and exited states
have been obtained. As an example, the perturbation expansions for the energy
eigenvalues of the harmonic oscillator perturbed by are
considered.Comment: 6 pages, LATEX 2.09 using IOP style
Exact Ampitude Ratio and Finite-Size Corrections for the M x N Square Lattice Ising Model The :
Let f, U and C represent, respectively, the free energy, the internal energy
and the specific heat of the critical Ising model on the square M x N lattice
with periodic boundary conditions. We find that N f and U are well-defined odd
function of 1/N. We also find that ratios of subdominant (N^(-2 i - 1))
finite-size corrections amplitudes for the internal energy and the specific
heat are constant. The free energy and the internal energy at the critical
point are calculated asymtotically up to N^(-5) order, and the specific heat up
to N^(-3) order.Comment: 18 pages, 4 figures, to be published in Phys. Rev. E 65, 1 February
200
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