17
Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625
INSOLVENCY FORECASTING THROUGH TREND ANALYSIS
WITHFULL IGNORANCE OFPROBABILITIES1
Tomáš Poláček, Ma ké a K un o ádo á*
Abs ac
The complex iews o  insol ency p oceedings a e unique, poo ly known, in e disciplina y
and mul idimensional, e en hough he e is a b oad spec um o  di e en BM (Bank up cy
Models). The e o e, i iso en p ohibi i ely di icul omake o ecas s using nume ical quan i ie s
and adi ional s a is ical me hods. Theleas in o ma ion-in ensi e end alues a eused: posi i e,
inc easing, ze o, cons an , nega i e, dec easing. Thesolu ion o a end model isase o scena ios
whe e X is hese o  a iables quan i ied by he ends. All possible ansi ions among hescena ios
a egene a ed. Ano ien ed ansi ional g aph has ase o scena ios asnodes and he ansi ions
asa cs. Ano ien ed pa h desc ibes any possible u u e andpas ime beha iou o  hebank up cy
sys em unde s udy. The g aph ep esen s he comple e lis o  o ecas s based on ends.
Aneigh -dimensional model se es asacase s udy. On he ansi ional g aph o  hecase s udy
model, decision ee heu is ics a eused o calcula ing hep obabili ies o  he e minal scena ios
andpossible payo s.
Keywo ds: o ecas , insol ency, end, quali a i e, bank up cy, ansi ion
JEL Classi ica ion: G33, G34
In oduc ion
A his ime, along wi h he inc easing numbe o insol ency p oceedings, e o s
a e being made o s eamline p ocesses and iden i y links be ween majo i y c edi o s
(M ázo á and Z i inský, 2015). These a e concu en wi h da a mining in es iga ions
o ind di e en ways o e ec i ely sol ing insol ency p oceedings in a ious egions
o he Czech Republic (M ázo á and Z i inský, 2014). Mo e and mo e p o essional
esea ch is conce ned wi h he ques ion o why he numbe o insol ency p oceedings
o bo h legal and na u al pe sons is inc easing (Paseko á and C ho á Kude o á, 2014).
Some s udies a e ocused on he desc ip i e s a e o he domes ic ma ke o e a ce ain
pe iod a e he in oduc ion o he Insol ency Ac (Sm čka, Schőn eld and Še čík, 2013)
o wha e ec he amendmen s and amendmen s o he ac i sel ha e on he p ac ice,
which add essed some o he undamen al issues ega ding powe s in decision-making
in insol ency p oceedings (Rich e , 2013). Few scien i ic s udies deal wi h he eco e y
o claims om insol ency p oceedings, o na u al o legal pe sons, o o p ac ical
solu ions o insol ency ha a ec a ious ma ke de e minan s (Jakubík, 2007).
1 This pape was suppo ed by g an s FP-S-18-5074 “De elopmen ends o he economic managemen
o he en e p ise in he Eu opean economic en i onmen ”.
* B no Uni e si y o Technology, Facul y o Business and Managemen (polacek@ bm. u b .cz;
k un o ado a@ bm. u b .cz).
18 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625
Insol ency p oceedings as such a e subjec o he in luence o many ac o s om
he whole economic en i onmen . Some ac o s (de e minan s) canno be quan i ied
and basic s a is ical models canno be used (Sen, Singe , 1994). So, he use o end esea ch
is app op ia e (Vícha and Dohnal, 2008; Dohnal, 2016). This means ha knowledge i ems
o di e en le els o subjec i i y mus be aken in o conside a ion o de elop he bes
possible model o a unique ask unde s udy. The e o e, many bank up cy obse a ions
a e equi ed. Howe e , hey a e no a ailable. This is he eason why in o ma ion
non-in ensi e o mal ools a e used mo e and mo e equen ly, see e.g. uzzy and/o ough
se s (Pa láko á Dočekalo á and Kocmano á, 2016; Meluzín e al., 2016).
1. Al e na i e Decision-Making Me hods in heP ocess
Decision-making analyses a e o en used o help decision-make s choose be ween
al e na i es based on he expec ed u ili y associa ed wi h he unc ion o i s consequences
and po en ial impac s. The e o e, o example, in a s udy (Wang e al., 2018) a mul ic i e ia
decision model is de eloped. Al hough many success ul s udies ha e been conduc ed
on he de ec ion o bank up cy, a ely ha e p obabilis ic app oaches been made.
In esea ch (An unes, Ribei o and Pe ei a, 2017), a p obabilis ic aspec is assumed
by applying Gaussian p ocesses. Bank up cy and eo ganisa ion p edic ion models
a e o en used in audi ing la ge co po a e ansac ions (me ge s and acquisi ions, s a egic
alliances, e c.), in making in es men decisions and in he judicia y, whe e judges a e inal
a bi a o s in bank up cy p oceedings.
Howe e , all exis ing insol ency models a e inadequa e mainly because he esea ch
me hods we e de ec i e. The au ho s me ely pu igid ma hema ical models in o
bank up cy. Models do no ollow an in e disciplina y app oach, do no allow op imisa ion
and simula ion o de i e he bes condi ions o minimising inancial h ea s. The s udy
(Nwogugu, 2006) p esen s a ious dynamic models o insol ency decision-making
and de elops he amewo k and basis o u he esea ch in o he use o dynamic sys ems
and a i icial in elligence in modelling bank up cy decisions and legal a gumen s.
This pape deals wi h bank up cy o ecas ing unde condi ions o se e e in o ma ion
sho ages. Such bank up cies a e o en desc ibed by non-nume ical quan i ie s, e.g. wo ds
– low, medium, high. Howe e , he ans e o such e bal alues in o uzzy se s is e y
subjec i e (Yi-Chung Hu and Tseng, 2007).
2. T end Models
The e a e many di e en in e p e a ions o end concep s (Kams and Kennedy, 1998;
S ekle and Syming on, 2016). The end concep s as i is used in his pape is based
on ou alues (Vicha and Dohnal, 2008; B edeweg, 2009):
Posi i e Ze o Nega i e Any Value (1)
+ 0 - *
An equa ionless end model M is a se o w pai -wise ela ions
M = Ps (Xi, Xj) (2)
s = 1, 2, ……w
19
Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625
Examples/shapes o he ela ions P (2) a e gi en in Figu e 1:
Figu e 1 | T ends ela ionships
Y
X
Y
X
Y
X
Y
X
Y
X
Y
X
25
25
25
26
22
23
33
33
3
26
24
22
21
21
23
25
22
24
26
X
Y
Y
Y
Y
Y
Y
X
X
X
X
X
Sou ce: Au ho s` own p ocessing
An algo i hm, which can be used o sol e he model (2), is based on he p uning
o a specially gene a ed ee o combina ions. I is no he goal o his pape o desc ibe
such an algo i hm, as i is a pu ely ma hema ical combina o ial ask (Vicha and Dohnal, 2008).
The model (2) is sol ed and he se o n dimensional scena ios is ob ained S(n, m).
The e a e m scena ios:
S(n, m) = (X1, DX1, DDX1), (X2, DX2, DDX2),…, (Xn, DXn, DDXn)j, (3)
j = 1, 2,…, m,
whe e DX is he i s and DDX is he second ime end de i a i es. Fo example,
he ollowing h ee-dimensional scena io, n = 3 (3).
X1 X2 X3 (4)
(+ + +) (+ - 0) (+ - -).
The model (2) is sol ed and he se o n dimensional scena ios is ob ained S(n, m).
The e a e m scena ios:
20 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625
2.1 T ansi ional G aphs
The se o scena ios S (3) is no he only esul o a end modelling. I is possible o gene a e
ansi ions among he se o scena ios.
Figu e 2 | A end desc ip ion o aquan i a i e oscilla ion
(+0-)
(0+0)
(+++)
(+0+)
(+--)
(+-+)
(0+0)
(++-)
Time
Sou ce: Au ho s` own p ocessing
The iple s gi en in Figu e 2 desc ibe a b oad spec um o di e en oscilla ions,
e.g. dumped oscilla ion o i egula oscilla ions wi h andomly o de e minis ically
changing equencies and/o ampli udes.
3. Case S udy
Based on he heu is ics o using end me hods, a iables ha ha e a majo impac
on he deb elie p ocess ha e been ca e ully selec ed a e discussions wi h insol ency
expe s. In he nex chap e , he a iables will be desc ibed wi h an explana ion o how
hei exis ence indi idually a ec s he insol ency p ocess. Subsequen ly, hese a iables
we e used o build a end model based on ime-dependen insol ency managemen
scena ios.
The e a e no published end models o bank up cies. A eam o wo expe s was
con ac ed and he lis o case s udy a iables was gene a ed:
SEL Selling o Asse s
ENJ Ensu ed Jus ice
GRD Le el o G eed
TAX Tax Bu den
SAT Sa is ac ion o C edi o s (5)
SOL Solu ion o Deb o s Asse s
POL Poli ical In luence
BUL Bullying o C edi o s
INF In la ion
21
Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625
Selling o asse s
In p inciple, i is igh ha a secu ed c edi o would decide on how he p ope y
o he c edi o is secu ed. Howe e , he p ac ice is mo e complex and e lec s a numbe
o pa ial in e es s o he subjec s who immedia ely decide on he me hod o mone isa ion
and, in his sense, hey ins uc he insol ency adminis a o . Al hough he insol ency
us ee may e use he o de s o he hedged c edi o i hey conside ha he objec
o he hedge can be mone ised mo e ad an ageously.
Ensu ed jus ice
I is a a iable ha ep esen s he mo al and ai beha iou o he insol ency cou , which
should pe o m a ca aly ic and independen ole in he insol ency p ocess. The insol ency
cou is he egional cou whe e he deb o `s insol ency p oceedings a e conduc ed.
I i is a legal en i y, i is a egional cou in he egion whe e he deb o is based. In he case
o a na u al pe son, i is he cou whe e he deb o esides.
Le el o g eed
The le el o g eed is a a iable unde s ood in end modelling as he i a ional beha iou
o he deb o , which pushes agains o he a iables o amo isa ion o he deb
and he sa is ac ion o he c edi o `s equi emen s. I has been selec ed as an impo an
ac o in he en i e insol ency p ocess and is also a sui able a iable o end modelling
in e ms o i s agueness and di icul y in quan i ying.
Tax bu den
Fo end modelling pu poses, he ax load a iable is applied as a con adic o y cons an
(depending on he ype o deb o /c edi o and he case o which he insol ency p oceedings
a e dedica ed). Unlike o he p ocess a iables, i is o a sha p na u e.
Sa is ac ion o c edi o s
Sa is ac ion o c edi o s is he i s o he a iables ha a e pe cei ed in he model
as a ge a iables o ep esen he bes possible s a e o he ques ion unde in es iga ion.
I is a ai paymen o deb s o c edi o s om deb o s whe e, based on he cou `s decision,
he c edi o (s) and c edi o commi ees a e spli in o secu ed and unsecu ed.
Solu ion o deb o asse s
In he end decision model, his a iable is seen as one o he goals ha should be as cos -
e ec i e as possible o he subjec , so ha he c edi o `s claim and he economic and social
s a us o he deb o a e main ained.
Poli ical in luence
I is no possible o analyse he coun y`s economy by only aking in o accoun ma ke
ac o s (Radu, 2015). E e y economic sys em mus be in eg a ed and ha monized
wi h he coun y`s con inuing de elopmen , a end ha e lec s echnological change
and inno a ion as well as poli ical con lic s ha lead o he ep esen a ion and changing
o di e en in e es s and ins i u ions. The e o e, i is impo an o include poli ical ac o s
o analyse he economic p ocess (Boye , 2011)

22 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625
Bullying o c edi o s
Being bullied by a c edi o is agains he law. Al hough c edi o s ha e many op ions
o claim hei igh o epaymen o he deb , which is conside ed legal, he e a e also many
p ac ices ha a e widely used ha a e no law ul (Ki wan, 2018). The ini ia ion o insol ency
p oceedings no only has nega i e legal consequences (e.g. limi ing he alleged deb o
in ela ion o he handling o his p ope y) bu also has non-legal consequences (damage
o he alleged deb o `s epu a ion, doub o his c edibili y and economic si ua ion).
In la ion
Simple in la ion e e s o an inc ease in he p ice le el. In e e yday li e, an inc ease
in in la ion may mean ha consume s pay mo e a a g oce y s o e o , o example,
a a pe ol s a ion (Vicki, 2017). Inc eased in la ion also a ec s se ices and hei
p o ide s. These ade s need o adjus hei se ice p ices adequa ely o in la iona y
de elopmen s because hei ising cos s a e dependen on inc easing supplie s` p ices
and can ha e a di ec e ec on he en i e deb o /c edi o sys em.
2.1 Model o Insol ency P oceedings
Build a iables (5), which play an impo an ole in he decision-making p ocess, and o m
a comple e se o scena ios, we e selec ed a e discussions wi h expe s on insol ency.
The e y na u e o he a iables used sugges s ha i is e y di icul o quan i y, see,
o example, GRD. The e o e, he use o end models is jus i ied.
See e.g. Figu e 1 T ends ela ionship 1, (1) X Y
1 + SEL ENJ
2 25 SEL GRD
3 21 SEL SAT
4 24 SEL SOL
5 23 ENJ TAX (6)
6 - ENJ BUL
7 + TAX POL
8 - SAT BUL
9 + POL INF
23
Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625
The e a e 23 scena ios, m = 23(6).
# SEL ENJ GRD TAX SAT SOL POL BUL INF
V V V V G G O O O
1 +++ +++ +-- +++ +++ +-+ +++ +-- +++
2 +++ +++ +-- +++ +++ +-0 +++ +-- +++
3 +++ +++ +-- +++ +++ +-- +++ +-- +++
4 +++ +++ +-- ++0 +++ +-+ ++0 +-- ++0
5 +++ +++ +-- ++0 +++ +-0 ++0 +-- ++0
6 +++ +++ +-- ++0 +++ +-- ++0 +-- ++0
7 +++ +++ +-- ++- +++ +-+ ++- +-- ++-
8 +++ +++ +-- ++- +++ +-0 ++- +-- ++-
9 +++ +++ +-- ++- +++ +-- ++- +-- ++-
10 ++- ++- +-+ ++- ++- +-+ ++- +-+ ++-
11 +0+ +0+ +0- +0+ +0+ +0- +0+ +0- +0+
12 +00 +00 +00 +00 +00 +00 +00 +00 +00 (7)
13 +0- +0- +0+ +0- +0- +0+ +0- +0+ +0-
14 +-+ +-+ ++- +-+ +-+ +++ +-+ ++- +-+
15 +-+ +-+ ++- +-+ +-+ ++0 +-+ ++- +-+
16 +-+ +-+ ++- +-+ +-+ ++- +-+ ++- +-+
17 +-+ +-+ ++- +-0 +-+ +++ +-0 ++- +-0
18 +-+ +-+ ++- +-0 +-+ ++0 +-0 ++- +-0
19 +-+ +-+ ++- +-0 +-+ ++- +-0 ++- +-0
20 +-+ +-+ ++- +-- +-+ +++ +-- ++- +--
21 +-+ +-+ ++- +-- +-+ ++0 +-- ++- +--
22 +-+ +-+ ++- +-- +-+ ++- +-- ++- +--
23 +-- +-- +++ +-- +-- +++ +-- +++ +--
Figu e 3 | T ansi ion g aph based onase o 23 scena ios (7)
10 13
23
12
16 15
11
19
22
21 20
17
18
14
7
4
8
3
9
6
2
5
1
Sou ce: Au ho s` own p ocessing
24 Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625
Any o ecas ing is hea ily p ede e mined by in e p e a ions o a iables (5).
The choice o he se s V, O, G, is o c ucial impo ance and is based on he cu en poin
o iew.
Any o ecas ing/decision-making will be based on an n-dimensional model M(X). A se
X o n a iables is a union o Decision a iables V, Goals a iables G and O -con ol
a iables O (8).
SEL V Selling o Asse s
ENJ V Ensu ed Jus ice
GRD V Le el o G eed
TAX O Tax
SAT G Sa is ac ion o he C edi o s (8)
SOL G Solu ion o Deb o `s Asse s
POL O Poli ical In luence
BUL V Bullying o C edi o s
INF O In la ion
O = [POL, INF, TAX]
G = [SAT, SOL] (9)
V = [SEL, ENJ, GRD, BUL]
A simple common-sense analysis indica es ha he e is one iew and o ecas om
he c edi o `s poin o iew:
Figu e 4 | C edi o `s iew – whe e ep esen s a a iable ime
SAT SOL
Sou ce: Au ho s` own p ocessing
The bes end desc ip ion o he c edi o `s iew:
SAT Inc ease mo e and mo e apidly DSAT = + DDSAT = +
SOL Dec easing mo e and mo e slowly DSOL = - DDSOL = + (10)
The wo s end desc ip ion o he c edi o `s iew:
SAT Dec easing mo e and mo e slowly DSAT = - DDSAT = +
SOL Inc ease mo e and mo e apidly DSOL = + DDSOL = + (11)
25
Ac a Oeconomica P agensia, 2019, 27(3–4), 17–30, h ps://doi.o g/10.18267/j.aop.625
The bes scena io is S7 (7). The sho es pa h is he pa h leading om he wo s
scena io S16 o he a ge scena io S7 (see Figu e 3):
S16 →S11 →S3 →S5 →S7 (12)
Figu e 5 | Asimpli ied ansi ion g aph based onase o 23 scena ios (7)
16 3 5 711
Sou ce: Au ho s` own p ocessing
The sequence o scena ios is, see (23):
No. SEL ENJ GRD TAX SAT SOL POL BUL INF
V V V V G G O O O
16 +-+ +-+ ++- +-+ +-+ ++- +-+ ++- +-+
11 +0+ +0+ +0- +0+ +0+ +0- +0+ +0- +0+ (13)
3 +++ +++ +-- +++ +++ +-- +++ +-- +++
5 +++ +++ +-- ++0 +++ +-0 ++0 +-- ++0
7 +++ +++ +-- ++- +++ +-+ ++- +-- ++-
A decision-make has no ee choice o change he a iables (5). Some a iables
a e no unde his/he con ol (8). The e o e, he e a e a iables selec ed by O as ou
o con ol. This means ha any o ecas is pa ially based on a ailable desc ip ions
o O a iables (13) e.g. p obabili y dis ibu ions.
3.2 P obabili y Dis ibu ions
Based on he ansi ional g aph om he case s udy in Figu e 5, he pa h om he wo s kind
o scena io o he bes kind o scena io acco ding o he c edi o ´s poin o iew was used.
The ansi ion g aph in Figu e 3 has been ans o med in o a decision ee whe e
some o he decision-making heu is ics can be used o ob aining he p obabili ies
and o de e mina e he o ecas . The esul ing e minal scena ios, which also e lec
he posi i e s a us o c edi o s, we e designa ed as e mina ion poin s. Whe e S16 was
designa ed as he oo node and S7 was he e mina ion node (wi h he o he s S1, S8 and S9).
Whe e he e mina ion scena ios ha e sligh ly di e en ou pu s.
Figu e 6 | The ansi ion g aph has been ans o med in o adecision ee (7)
2
16
1
7
89
5
4
3
11
6
Sou ce: Au ho s` own p ocessing