ABSTRACTS

This international conference is supported by the Ministry of Education, Culture, Sports, Scienceand Technology(MEXT) “Coop with Math Program.”
本国際会議は、文部科学省「数学・数理科学と諸科学・産業との協働によるイノベーション創出のための研究促進プログラム」の助成を受けています。

URL: http://www.jafee.gr.jp/01rally/jafee columbia ism.html

March 18, Monday
Chair of the day: Takaki Hayashi (Keio Univ.)
09:50-09:55

Opening Remark

1st. Session / Chair: Yoichi Nishiyama (The Institute of Statistical Mathematics)
10:00-10:50 Shigeo Kusuoka (The University of Tokyo)“A remark on credit risk models and copula”
10:50-11:30 Hongzhong Zhang (Columbia University)“Quickest detection in a system with correlated noise”
11:30-13:00

Lunch break

2nd. Session / Chair: Yuji Yamada (Tsukuba University)
13:00-13:50 Eckhard Platen (University of Technology, Sydney)“Benchmarked Risk Minimization”
13:50-14:30 Hideatsu Tsukahara (Seijo University)“Risk Management with Distortion Risk Measures”
14:30-15:10 Andrew Lim (National University of Singapore & University of California at
Berkeley)“Optimal dynamic portfolio choice with multiple decentralized agents”
15:10-15:30

Coﬀee Break3rd. Session / Chair: Hongzhong Zhang (Columbia University)
15:30-16:20 Takeaki Kariya (Meiji University)“Measuring Credit Risk of French, Italian, Spanish and Greek GBs Relative
to German GB and Deriving Term Structures of Default Probabilities”
16:20-17:00 Toshinao Yoshiba (Bank of Japan)“Analytical solutions for expected loss and standard deviation of loss with anadditional loan”
17:00-17:40 Yuji Morimoto (Capitas Consulting Corporation)“Current topics regarding risk management practice in ﬁnance and insurance”
18:00-20:00

Reception2

March 19, Tuesday
Chair of the day: Satoshi Yamashita (ISM)
1st. Session / Chair: Jiro Akahori (Ritsumeikan University)
10:00-10:50 Philip Protter (Columbia University)“Can one detect a ﬁnancial bubble in real time?”
10:50-11:30 Masaaki Fukasawa (Osaka University)“Eﬃcient Discretization of Stochastic Integrals”
11:30-13:00

Lunch break

2nd. Session / Chair: Masaaki Fukasawa (Osaka University)
13:00-13:50 Short communication
Takanori Adachi (ICS, Hitotsubashi University)“A note on categorical risk measure theory”
Nienlin Liu (Ritsumeikan University)“The Fourier estimation method based on discrete Fourier transform”
13:50-14:30 Cecilia Mancini (University of Florence)“Measuring the relevance of the microstructure noise in ﬁnancial data”
14:30-15:10 Yoshinori Kawasaki (The Institute of Statistical Mathematics)“Yield curve estimation using both bid and ask prices of coupon bonds”
15:10-15:30

Coﬀee Break3rd. Session / Chair: Hideatsu Tsukahara (Seijo University)
15:30-16:20 Richard A. Davis (Columbia University)“Noncausal Vector AR Processes with Application to Financial Time Series”
16:20-17:00 Yoichi Nishiyama (The Institute of Statistical Mathematics)“On Entropy-Martingale Methods in Statistics”
17:00-17:40 Peter Spreij (University of Amsterdam)“Aﬃne diﬀusions with non-canonical state space”
17:40-17:45

Closing Remark

3Shigeo Kusuoka
The University of Tokyo

A remark on credit risk models and copula
Abstract
Copula models with ﬁnite parameters are widely used to describe the joint distribution of default
times. But it is not clear whether these copula models are dynamically consistent. The authors
show that the set of copula models that are dynamically consistent and satisfy some technicalregularity conditions, is a set of the ﬁrst category in the Baire sense in a certain space of copulafunctions with ﬁnite parameters.
(Joint work with Takenobu Nakashima)

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Hongzhong Zhang
Columbia University

Quickest detection in a system with correlated noise
Abstract
The problem of quickest detection arises in many applications in quality control and ﬁnancial
surveillance. In this work, we study the quickest detection of signals in a system of 2 sensors
coupled by a negatively correlated noise, which receive continuous sequential observations from theenvironment. It is assumed that the signals are time invariant and with equal strength, but that
their onset times may diﬀer from sensor to sensor. The objective is the optimal detection of theﬁrst time at which any sensor in the system receives a signal. The problem is formulated as astochastic optimization problem in which an extended Lorden’s criterion is used as a measure ofdetection delay, with a constraint on the mean time to the ﬁrst false alarm. The case in which thesensors employ their own cumulative sum (CUSUM)strategies is considered, and it is proved thatthe minimum of 2 CUSUMs is asymptotically optimal as the mean time to the ﬁrst false alarmincreases without bound. Implications of this asymptotic optimality result to the eﬃciency of thedecentralized versus the centralized system of observations are further discussed.

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Eckhard Platen
University of Technology Sydney

Benchmarked risk minimization
Abstract
This paper discusses the problem of hedging not perfectly replicable contingent claims using
the numeraire portfolio. The proposed concept of benchmarked risk minimization generalizes classical risk minimization, pioneered by Foellmer, Sondermann and Schweizer. The latter relies on aquadratic criterion, requests square integrability of contingent claims, assumes certain martingale
properties and relies on the existence of an equivalent risk neutral probability measure. Benchmarked risk minimization avoids these restrictive assumptions and provides symmetry with respect
to all primary securities. It employs the real world probability measure and the numeraire portfolio to identify the minimal possible price for a contingent claim. Furthermore, the resulting
benchmarked (i.e. numeraire-denominated) proﬁt and loss is only driven by uncertainty that is
orthogonal to traded uncertainty, and forms a local martingale that starts at zero. Consequently,
benchmarked proﬁts and losses, when pooled and suﬃciently diﬀerent, become asymptotically negligible through diversiﬁcation. This property is highly desirable from a risk management point ofview. It makes benchmarked risk minimization the least expensive method for pricing and hedging
a diversiﬁed pool of not fully replicable benchmarked contingent claims. Finally, a benchmarked
risk minimizing hedging strategy takes into account evolving information about the nonhedgeablepart of a contingent claim, which classical risk minimization ignores.
(Joint work with Ke Du)

6Hideatsu Tsukahara
Seijo University

Risk management with distortion risk measures
Abstract
We have shown in our previous work that for a wide class of distortion functions, it is possible
to construct an estimator for distortion risk measures (DRMs) with reasonable accuracy based on
weakly dependent data. In this presentation, we ﬁrst show that the estimator always has a negative
bias and illustrate a bootstrap-based method for bias correction. The method will be shown topossess consistency under a certain regularity condition. For a Monte Carlo simulation study, we
consider a stochastic volatility (SV) model with inverse gamma AR(1) volatility process. Simulation
results for estimating value-at-risk, expected shortfall and proportional odds risk measure undervarious values of the parameters show that the normal approximation, our asymptotic varianceestimation and bias correction methods are working to a reasonable extent.
As a next step in ﬁnancial risk management, we need to evaluate the accuracy of the model
and/or estimation procedure for risk measurement. To this end, a simple backtesting procedures
will be proposed for DRMs which can be made theoretically rigorous with i.i.d. data. We can also
implement the conditional approach by McNeil and Frey with GARCH-type observations. As acapital allocation principle, the Euler allocation based on DRMs are easy to compute and widely
applicable. We give some numerical results for the comparison of the Euler allocation with several
DRMs under some scenarios on the loss distribution. The portfolio optimization problem with
DRMs following Acerbi is now being investigated; how to implement numerically is one of theremaining issues on DRMs.

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Andrew Lim
National University of Singapore & University of California at Berkeley

Optimal dynamic portfolio choice with multiple decentralized agents
Abstract
While the primary concern of many ﬁnancial institutions is the aggregate performance of its
trades, centralized optimization over all asset holdings across multiple correlated markets is infeasible in practice due to the complexity of the system and each of the constituent markets, and adecentralized approach where trades in each market are optimized by a diﬀerent portfolio manager
conditional on a proprietary model of his investment universe, is more commonly adopted. The
diﬃculty with this approach is that the resulting collection of “locally optimized” allocations canbe extremely ineﬃcient from the perspective of the ﬁrm. In this paper, we formulate a multiagent dynamic portfolio choice problem and study the problem of optimizing system eﬃciency. We
show that a coordination mechanism consisting of an internal system of swap contracts can induce
decentralized allocations that as a collection are optimal for the ﬁrm. We provide a characterization of the optimal contract and an iterative algorithm for computing it. This algorithm canbe implemented without compromising proprietary agent level information or intervention by an
all-knowing centralized agent, and only uses data that is commonly reported as part of a ﬁrm’s risk
management system.

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Takeaki Kariya
Meiji University

Measuring credit risk of French, Italian, Spanish, and Greek GBs
relative to German GBs, and deriving the term structuresof default probabilities (TSGBs)
Abstract
Applying the Kariya s (2012) model to Euro government bonds, we make a relative credit risk
analysis on the credit risk of French, Italian, Spanish, and Greek GBs relative to German GBs.
First we measure credit risk spreads of these GBs in price level over four years. Then their TSDPs
are derived relative to DGB prices with recovery rate being assumed as 0. Thirdly an almost
perfect linear relationship between interest diﬀerentials and default probabilities is observed withdiscussion on the Maastricht convergence condition.
(Joint work with Yoshiro Yamamura, Koji Inui, Yoko Tanokura, ZhuWang)

9Toshinao Yoshiba
Bank of Japan

Analytical solutions for expected loss andstandard deviation of loss with an additional loan
Abstract
We evaluate expected loss and standard deviation of loss for a bank loan, taking into accountthe bank s strategic control of the expected return on the loan. Assuming that the bank supplies anadditional loan to minimize the expected loss of the total loan, we provide analytical formulations
for expected loss and standard deviation of loss with bivariate normal distribution functions.
There are two cases in which an additional loan decreases the expected loss: i) the asset/liability
ratio of the ﬁrm is low but its expected growth rate is high; ii) the asset/liability ratio of the ﬁrm
is high and the lending interest rate is high. With a given expected growth rate and given interest
rates, the two cases are identiﬁed by two thresholds for the current asset/liability ratio. The bankmaintains the current loan amount when the asset/liability ratio is between the two thresholds.
Given the bank s strategy, the bank decreases the initial expected loss of the loan. On theother hand, the bank has a greater risk for the standard deviation of loss. (Joint work with Satoshi
Yamashita.)

Keywords: Probability of default (PD); Loss given default (LGD); Exposure at default (EaD);
Expected loss (EL); Unexpected loss (UL); Structural model

10

Yuji Morimoto
Capitas Consulting Corporation

Current topics regarding risk management practicein ﬁnance and insurance
Abstract
In this session, I will overview the current topics and issues in the risk management practices inﬁnance and insurance. First, I will introduce the current status of the risk management practice byshowing the selected results of the survey conducted by TRMA (Tokyo Risk Managers Association)
last year. Then, I will explain the risk management issues in the insurance industry so called
ERM (Enterprise Risk Management), which the regulatory body is introducing as a tool for thesupervision of ﬁnancial institutions. In the second topic, various kinds of quantitative issues areincluded, although many of them have not been deeply researched yet and many practitioners
do not know the pitfalls or caveats for implementing the techniques into risk management. The
objective of this talk is to share these issues with academics of various ﬁelds and hopefully to getsolutions for some issues in near future.

———————————
President of the Capitas Consulting Corporation, Hamarikyu Parkside Place 5F, 5-6-10, Tsukiji, Chuo-ku, Tokyo
104-0045, JAPAN. Email: ymorimoto@capitas.jp

11Philip Protter
Columbia University

Can one detect a ﬁnancial bubble in real time?
Abstract
Recent advances in the mathematical modeling of ﬁnancial bubbles have led to the observationthat bubble detection often boils down to determining if, under the risk neutral measure, a process
is a strict local martingale or a true martingale. Bubbles are fairly easily recognizable after thefact, once they have run their course, but it is often diﬃcult to detect their presence in real time.
There are few tools available to distinguish a martingale from a strict local martingale, and it seems
that determining which is the case from data is a delicate procedure. Indeed, one can argue thatin principle it is impossible. Nevertheless in this talk we will explain how, in a special case, there
is hope that one can determine when a bubble is present, and when it is not, in real time.
(Joint work with Robert Jarrow and Younes Kchia)

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Masaaki Fukasawa
Osaka University

Eﬃcient discretization of stochastic integrals
Abstract
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error instochastic integration are given when the integrator admits a predictable quadratic variation and theintegrand is a continuous semimartingale with nondegenerate local martingale part. Asymptoticallyeﬃcient schemes which attain the lower bounds are constructed explicitly.
The result is directly applicable to practical hedging problem in mathematical ﬁnance; forhedging a payoﬀ which is replicated by a continuous-time trading strategy, it gives an asymptotically
optimal way to choose discrete rebalancing dates and portfolios with respect to transaction costs.
The asymptotically eﬃcient strategies in fact reﬂect the structure of transaction costs. In particulara speciﬁc biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs
follow a convex model.

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Short Communication
Takanori Adachi (ICS, Hitotsubashi University)

A note on categorical risk measure theory
Abstract
We introduce a category that represents varying risk as well as uncertainty, and give a generalized conditional expectation as a contravariant functor on the category. Then, we re formulate
dynamic monetary value measures as a contravariant functor on the category. We show some axioms of dynamic monetary value measures in the classical setting are deduced as theorems in the
new formulation, which may be one of the evidences that the axioms are natural.

Nienlin Liu (Ritsumeikan University)

The Fourier estimation method based on discrete Fourier transform
Abstract
In the talk, we will introduce another version of Fourier estimation method, which is basedon discrete Fourier transform. Thanks to the group structure, the estimator is always positive(deﬁnite) and the consistency is easier to prove.
(Joint work with Jiro Akahori, Yukie Yasuda and Maria Elvira Mancino)

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Cecilia Mancini
University of Florence

Measuring the relevance of the microstructure noisein ﬁnancial data
Abstract
We show that the Truncated Realized Variance (TRV) of a semimartingale converges to zero
when observations are contaminated by noise. Under the additive iid noise assumption, a central
limit theorem is also proved. In consequence it is possible to construct a feasible test allowing us tomeasure, for a given path of a given data generating process at a given observation frequency, therelevance of the noise in the data when we want to estimate the eﬃcient process integrated variance
IV. We thus can optimally select the observation frequency at which we can ”safely” use TRV. The
local size of our test is investigated and its performance is veriﬁed on simulated data. We areespecially interested in the application of the test to ﬁnancial data, and a comparison conducted on
the one hand with the Bandi and Russel (2008) and Ait-Sahalia, Mykland and Zhang (2005) meansquare error criterions and on the other hand with the Realized Variance (RV) signature plot, showsthat, in order to estimate IV, in many cases we can rely on TRV for lower observation frequencies
than previously indicated when using RV. The advantages of our method are at least two: on the
one hand the underlying model for the eﬃcient data generating process is less restrictive in thatjumps are allowed (in the form of an Ito semimartingale, SM). On the other hand our criterion ispathwise, rather than based on an average estimation error, allowing for a more precise estimationof IV because the choice of the optimal frequency is based on the observed path. Further analysis
on both simulated and empirical ﬁnancial data is conducted in [Lorenzini 2012] and is also still inprogress.
Keywords: semimartingales with jumps, noisy data, integrated variance, threshold estimation, test to select optimal
sampling frequency, financial asset prices

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Yoshinori Kawasaki
The Institute of Statistical Mathematics

Yield curve estimation using both bid and ask pricesof coupon bonds
Abstract
We consider the problem of estimating yield curves utilizing both bid and ask prices of coupon
bonds. Many of the existing research in this literature are based on the closing price. With oureyes set on a real-time base inference during trading hours, we work on both bid and ask data forevery traded bond. For a coupon bond we sometimes observe either bid or ask price only, whileat other occasions we may ﬁnd both prices at a time. A collection of such bond data naturally
leads to nonparametric-regression-type yield curve estimation. After observing that the smoothing
spline ANOVA framework properly ﬁts this multiple curve estimation problem, we show that it ispossible to estimate yield curves that are simultaneously coherent with bid and ask prices.
(Joint work with Yasunori Horikoshi.)16

Richard A. Davis
Columbia University

Noncausal Vector AR processes
with application to ﬁnancial time series
Abstract
Inference procedures for noncausal autoregressive (AR) models have been well studied andapplied in a variety of applications from environmental to ﬁnancial. For such processes, the observations at time t may depend on both past and future shocks in the system. In this paper, weconsider extension of the univariate noncausal AR models to the vector AR (VAR) case. The extension presents several interesting challenges since even a ﬁrst-order VAR can possess both causal
and noncausal components. Assuming a non-Gaussian distribution for the noise, we show how tocompute an approximation to the likelihood function. Under suitable conditions, it is shown thatthe maximum likelihood estimator (MLE) of the vector of AR parameters is asymptotically normal.
The estimation procedure is illustrated with a simulation study for a VAR(1) process and with tworeal data examples.
(Joint work with Li Song)17

Yoichi Nishiyama
The Institute of Statistical Mathematics

On entropy-martingale methods in statistics
Abstract
The title of my talk is the same as that of my forthcoming book to be published by Chapman& Hall. My talk will be based on my own results that would be contained in my book, including
some topics of a stochastic maximal inequality as an extension of Doob’s inequality, some inﬁnitedimensional Lenglart’s and Burkholder’s inequalities, some central limit theorems for separable
random ﬁelds of locally square-integrable martingales including a new Donsker theorem for functionindexed empirical processes of i.i.d. samples under a bit stronger condition than Sudakov’s suﬃcientcondition for the existence of bounded continuous versions of general Gaussian random ﬁelds and the(probably) ﬁnal version of the Jain-Marcus theorems for the sum of i.i.d. Lipschitz random ﬁelds,
and a semiparametric Z-estimation procedure, which would often yield some adaptive estimators,
with applications to Cox’s regression model and an ergodic diﬀusion process model with highfrequency data.

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Peter Spreij
University of Amsterdam

Aﬃne diﬀusions with non-canonical state space
Abstract
Multidimensional aﬃne diﬀusions have been studied in detail for the case of a canonical state
space. We present results for general (convex) state spaces and provide a complete characterizationof all possible aﬃne diﬀusions with polyhedral and quadratic state space. We give necessary andsuﬃcient conditions on the behavior of drift and diﬀusion on the boundary of the state space inorder to obtain invariance and to establish strong existence and uniqueness. If time permits, wewill discuss existence of exponential moments and the validity of the aﬃne transform formula forprocesses with a general closed convex state space. Our results apply to a wide class of aﬃneprocesses, including those with a matrix-valued state space, which have recently gained interest in
the literature.
(Joint work with Enno Veerman)

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